class Graph(GraphBase):
Generic graph.
This class is built on top of GraphBase
, so the order of the methods in the generated API documentation is a little bit obscure: inherited methods come after the ones implemented directly in the subclass. Graph
provides many functions that GraphBase
does not, mostly because these functions are not speed critical and they were easier to implement in Python than in pure C. An example is the attribute handling in the constructor: the constructor of Graph
accepts three dictionaries corresponding to the graph, vertex and edge attributes while the constructor of GraphBase
does not. This extension was needed to make Graph
serializable through the pickle module. Graph
also overrides some functions from GraphBase
to provide a more convenient interface; e.g., layout functions return a Layout
instance from Graph
instead of a list of coordinate pairs.
Graphs can also be indexed by strings or pairs of vertex indices or vertex names. When a graph is indexed by a string, the operation translates to the retrieval, creation, modification or deletion of a graph attribute:
>>> g = Graph.Full(3) >>> g["name"] = "Triangle graph" >>> g["name"] 'Triangle graph' >>> del g["name"]
When a graph is indexed by a pair of vertex indices or names, the graph itself is treated as an adjacency matrix and the corresponding cell of the matrix is returned:
>>> g = Graph.Full(3) >>> g.vs["name"] = ["A", "B", "C"] >>> g[1, 2] 1 >>> g["A", "B"] 1 >>> g["A", "B"] = 0 >>> g.ecount() 2
Assigning values different from zero or one to the adjacency matrix will be translated to one, unless the graph is weighted, in which case the numbers will be treated as weights:
>>> g.is_weighted() False >>> g["A", "B"] = 2 >>> g["A", "B"] 1 >>> g.es["weight"] = 1.0 >>> g.is_weighted() True >>> g["A", "B"] = 2 >>> g["A", "B"] 2 >>> g.es["weight"] [1.0, 1.0, 2]
Class Method 

Generates a graph from its adjacency matrix. 
Class Method 

Creates a bipartite graph with the given vertex types and edges. This is similar to the default constructor of the graph, the only difference is that it checks whether all the edges go between the two vertex classes and it assigns the type vector to a ... 
Class Method 

Generates a graph from one or two dataframes. 
Class Method 

Constructs a graph from a listofdictionaries representation. 
Class Method  from 
Converts the graph from graphtool 
Class Method  from 
Converts the graph from networkx 
Class Method 

Generates a full bipartite graph (directed or undirected, with or without loops). 
Class Method  GRG 
Generates a random geometric graph. 
Class Method 

Creates a bipartite graph from an incidence matrix. 
Class Method 

Generates a random bipartite graph with the given number of vertices and edges (if m is given), or with the given number of vertices and the given connection probability (if p is given). 
Class Method 

Unified reading function for graphs. 
Class Method 

Constructs a graph based on an adjacency matrix from the given file. 
Class Method 

Reads a graph from a file conforming to the DIMACS minimumcost flow file format. 
Class Method 

Reads a graph from a zipped GraphML file. 
Class Method 

Reads a graph from Python pickled format 
Class Method 

Reads a graph from compressed Python pickled format, uncompressing it onthefly. 
Class Method 

Constructs a graph from a listoftuples representation. 
Class Method 

Generates a graph from its weighted adjacency matrix. 
Method  __add__ 
Copies the graph and extends the copy depending on the type of the other object given. 
Method  __and__ 
Graph intersection operator. 
Method  __bool__ 
Returns True if the graph has at least one vertex, False otherwise. 
Method  __coerce__ 
Coercion rules. 
Method  __iadd__ 
Inplace addition (disjoint union). 
Method  __init__ 
__init__(n=0, edges=None, directed=False, graph_attrs=None, vertex_attrs=None, edge_attrs=None) 
Method  __isub__ 
Inplace subtraction (difference). 
Method  __mul__ 
Copies exact replicas of the original graph an arbitrary number of times. 
Method  __or__ 
Graph union operator. 
Method  __plot__ 
Plots the graph to the given Cairo context in the given bounding box 
Method  __reduce__ 
Support for pickling. 
Method  __str__ 
Returns a string representation of the graph. 
Method  __sub__ 
Removes the given object(s) from the graph 
Method  add 
Adds a single edge to the graph. 
Method  add 
Adds some edges to the graph. 
Method  add 
Adds a single vertex to the graph. Keyword arguments will be assigned as vertex attributes. Note that name as a keyword argument is treated specially; if a graph has name as a vertex attribute, it allows one to refer to vertices by their names in most places where igraph expects a vertex ID. 
Method  add 
Adds some vertices to the graph. 
Method  all 
Returns all the cuts between the source and target vertices in a directed graph. 
Method  all 
Returns all the mincuts between the source and target vertices in a directed graph. 
Method  as 
Returns a directed copy of this graph. Arguments are passed on to to_directed() that is invoked on the copy. 
Method  as 
Returns an undirected copy of this graph. Arguments are passed on to to_undirected() that is invoked on the copy. 
Method  biconnected 
Calculates the biconnected components of the graph. 
Method  bipartite 
Projects a bipartite graph into two onemode graphs. Edge directions are ignored while projecting. 
Method  bipartite 
Calculates the number of vertices and edges in the bipartite projections of this graph according to the specified vertex types. This is useful if you have a bipartite graph and you want to estimate the amount of memory you would need to calculate the projections themselves. 
Method  clear 
Clears the graph, deleting all vertices, edges, and attributes. 
Method  clusters 
Calculates the (strong or weak) clusters (connected components) for a given graph. 
Method  cohesive 
Calculates the cohesive block structure of the graph. 
Method  community 
Community structure based on the betweenness of the edges in the network. 
Method  community 
Community structure based on the greedy optimization of modularity. 
Method  community 
Finds the community structure of the network according to the Infomap method of Martin Rosvall and Carl T. Bergstrom. 
Method  community 
Finds the community structure of the graph according to the label propagation method of Raghavan et al. 
Method  community 
Newman's leading eigenvector method for detecting community structure. 
Method  community 
Naive implementation of Newman's eigenvector community structure detection. 
Method  community 
Finds the community structure of the graph using the Leiden algorithm of Traag, van Eck & Waltman. 
Method  community 
Community structure based on the multilevel algorithm of Blondel et al. 
Method  community 
Calculates the optimal modularity score of the graph and the corresponding community structure. 
Method  community 
Finds the community structure of the graph according to the spinglass community detection method of Reichardt & Bornholdt. 
Method  community 
Community detection algorithm of Latapy & Pons, based on random walks. 
Method  count 
Returns the number of automorphisms of the graph. 
Method  degree 
Calculates the degree distribution of the graph. 
Method  delete 
Deletes some edges from the graph. 
Method  dfs 
Conducts a depth first search (DFS) on the graph. 
Method  disjoint 
Creates the disjoint union of two (or more) graphs. 
Method  dyad 
Calculates the dyad census of the graph. 
Method  get 
Returns the adjacency matrix of a graph. 
Method  get 
Returns the adjacency matrix of a graph as a SciPy CSR matrix. 
Method  get 
Returns the adjacency list representation of the graph. 
Method  get 
Calculates all the simple paths from a given node to some other nodes (or all of them) in a graph. 
Method  get 
Returns all the automorphisms of the graph 
Method  get 
Export edges with attributes to pandas.DataFrame 
Method  get 
Returns the incidence matrix of a bipartite graph. The incidence matrix is an n times m matrix, where n and m are the number of vertices in the two vertex classes. 
Method  get 
Returns the incidence list representation of the graph. 
Method  get 
Export vertices with attributes to pandas.DataFrame 
Method  gomory 
Calculates the GomoryHu tree of an undirected graph with optional edge capacities. 
Method  indegree 
Returns the indegrees in a list. 
Method  intersection 
Creates the intersection of two (or more) graphs. 
Method  is 
Returns whether the graph is named. 
Method  is 
Returns whether the graph is weighted. 
Method  k 
Returns some kcores of the graph. 
Method  layout 
Returns the layout of the graph according to a layout algorithm. 
Method  layout 
Chooses and runs a suitable layout function based on simple topological properties of the graph. 
Method  layout 
Places the vertices using a layered Sugiyama layout. 
Method  maxflow 
Returns a maximum flow between the given source and target vertices in a graph. 
Method  maximum 
Finds a maximum matching in a bipartite graph. 
Method  mincut 
Calculates the minimum cut between the given source and target vertices or within the whole graph. 
Method  modularity 
Calculates the modularity score of the graph with respect to a given clustering. 
Method  outdegree 
Returns the outdegrees in a list. 
Method  pagerank 
Calculates the PageRank values of a graph. 
Method  path 
Returns the path length histogram of the graph 
Method  spanning 
Calculates a minimum spanning tree for a graph. 
Method  st 
Calculates the minimum cut between the source and target vertices in a graph. 
Method  summary 
Returns the summary of the graph. 
Method  to 
Converts the graph to graphtool 
Method  to 
Converts the graph to networkx format. 
Method  transitivity 
Calculates the average of the vertex transitivities of the graph. 
Method  triad 
Calculates the triad census of the graph. 
Method  union 
Creates the union of two (or more) graphs. 
Method  write 
Unified writing function for graphs. 
Method  write 
Writes the adjacency matrix of the graph to the given file 
Method  write 
Writes the graph in DIMACS format to the given file. 
Method  write 
Writes the graph to a zipped GraphML file. 
Method  write 
Saves the graph in Python pickled format 
Method  write 
Saves the graph in Python pickled format, compressed with gzip. 
Method  write 
Saves the graph as an SVG (Scalable Vector Graphics) file 
Class Variable  __hash__ 
Undocumented 
Class Variable  __iter__ 
Undocumented 
Class Variable 

Undocumented 
Property  es 
The edge sequence of the graph 
Property  vs 
The vertex sequence of the graph 
Class Method  _identify 
_identify_format(filename) 
Class Method  _reconstruct 
Reconstructs a Graph object from Python's pickled format. 
Class Variable  _format 
Undocumented 
Class Variable  _layout 
Undocumented 
Property  _as 
Undocumented 
Inherited from GraphBase
:
Method  __new__ 
Create and return a new object. See help(type) for accurate signature. 
Method  all 
Returns a list containing all the minimal st separators of a graph. 
Method  are 
Decides whether two given vertices are directly connected. 
Method  articulation 
Returns the list of articulation points in the graph. 
Method  assortativity 
Returns the assortativity of the graph based on numeric properties of the vertices. 
Method  assortativity 
Returns the assortativity of a graph based on vertex degrees. 
Method  assortativity 
Returns the assortativity of the graph based on vertex categories. 
Method 

Generates a graph based on asymmetric vertex types and connection probabilities. 
Method 

Generates a graph from the Graph Atlas. 
Method  attributes 
No summary 
Method  authority 
Calculates Kleinberg's authority score for the vertices of the graph 
Method  average 
Calculates the average path length in a graph. 
Method 

Generates a graph based on the BarabasiAlbert model. 
Method  betweenness 
Calculates or estimates the betweenness of vertices in a graph. 
Method  bfs 
Conducts a breadth first search (BFS) on the graph. 
Method  bfsiter 
Constructs a breadth first search (BFS) iterator of the graph. 
Method  bibcoupling 
Calculates bibliographic coupling scores for given vertices in a graph. 
Method  bridges 
Returns the list of bridges in the graph. 
Method  canonical 
Calculates the canonical permutation of a graph using the BLISS isomorphism algorithm. 
Method  clique 
Returns the clique number of the graph. 
Method  cliques 
Returns some or all cliques of the graph as a list of tuples. 
Method  closeness 
Calculates the closeness centralities of given vertices in a graph. 
Method  cocitation 
Calculates cocitation scores for given vertices in a graph. 
Method  complementer 
Returns the complementer of the graph 
Method  compose 
Returns the composition of two graphs. 
Method  constraint 
Calculates Burt's constraint scores for given vertices in a graph. 
Method  contract 
Contracts some vertices in the graph, i.e. replaces groups of vertices with single vertices. Edges are not affected. 
Method  convergence 
Undocumented (yet). 
Method  convergence 
Undocumented (yet). 
Method  copy 
Creates a copy of the graph. 
Method  coreness 
Finds the coreness (shell index) of the vertices of the network. 
Method  count 
Determines the number of isomorphisms between the graph and another one 
Method  count 
Counts the multiplicities of the given edges. 
Method  count 
Determines the number of subisomorphisms between the graph and another one 
Method 

Generates a de Bruijn graph with parameters (m, n) 
Method  decompose 
Decomposes the graph into subgraphs. 
Method  degree 
Returns some vertex degrees from the graph. 
Method 

Generates a graph with a given degree sequence. 
Method  delete 
Deletes vertices and all its edges from the graph. 
Method  density 
Calculates the density of the graph. 
Method  dfsiter 
Constructs a depth first search (DFS) iterator of the graph. 
Method  diameter 
Calculates the diameter of the graph. 
Method  difference 
Subtracts the given graph from the original 
Method  diversity 
Calculates the structural diversity index of the vertices. 
Method  dominator 
Returns the dominator tree from the given root node 
Method  eccentricity 
Calculates the eccentricities of given vertices in a graph. 
Method  ecount 
Counts the number of edges. 
Method  edge 
No summary 
Method  edge 
Calculates or estimates the edge betweennesses in a graph. 
Method  edge 
Calculates the edge connectivity of the graph or between some vertices. 
Method  eigen 
Undocumented 
Method  eigenvector 
Calculates the eigenvector centralities of the vertices in a graph. 
Method 

Generates a graph based on the ErdosRenyi model. 
Method 

Generates a graph based on a simple growing model with vertex types. 
Method 

Generates a famous graph based on its name. 
Method  farthest 
Returns two vertex IDs whose distance equals the actual diameter of the graph. 
Method  feedback 
Calculates an approximately or exactly minimal feedback arc set. 
Method 

Generates a graph based on the forest fire model 
Method 

Generates a full graph (directed or undirected, with or without loops). 
Method 

Generates a full citation graph 
Method  get 
Calculates all of the shortest paths from/to a given node in a graph. 
Method  get 
Returns a path with the actual diameter of the graph. 
Method  get 
Returns the edge list of a graph. 
Method  get 
Returns the edge ID of an arbitrary edge between vertices v1 and v2 
Method  get 
Returns the edge IDs of some edges between some vertices. 
Method  get 
Returns all isomorphisms between the graph and another one 
Method  get 
Calculates the shortest paths from/to a given node in a graph. 
Method  get 
Returns all subisomorphisms between the graph and another one using the LAD algorithm. 
Method  get 
Returns all subisomorphisms between the graph and another one 
Method  girth 
Returns the girth of the graph. 
Method 

Generates a growing random graph. 
Method  harmonic 
Calculates the harmonic centralities of given vertices in a graph. 
Method  has 
Checks whether the graph has multiple edges. 
Method  hub 
Calculates Kleinberg's hub score for the vertices of the graph 
Method  incident 
Returns the edges a given vertex is incident on. 
Method  independence 
Returns the independence number of the graph. 
Method  independent 
Returns some or all independent vertex sets of the graph as a list of tuples. 
Method  induced 
Returns a subgraph spanned by the given vertices. 
Method  is 
Decides whether the graph is bipartite or not. 
Method  is 
Decides whether the graph is connected. 
Method  is 
Checks whether the graph is a DAG (directed acyclic graph). 
Method  is 
Checks whether the graph is directed. 
Method  is 
Checks whether a specific set of edges contain loop edges 
Method  is 
Decides whether the given vertex set is a minimal separator. 
Method  is 
Checks whether an edge is a multiple edge. 
Method  is 
Checks whether an edge has an opposite pair. 
Method  is 
Decides whether the removal of the given vertices disconnects the graph. 
Method  is 
Checks whether the graph is simple (no loop or multiple edges). 
Method  is 
Checks whether the graph is a (directed or undirected) tree graph. 
Method 

Generates a graph with a given isomorphism class. 
Method  isoclass 
Returns the isomorphism class of the graph or its subgraph. 
Method  isomorphic 
Checks whether the graph is isomorphic to another graph. 
Method  isomorphic 
Checks whether the graph is isomorphic to another graph, using the BLISS isomorphism algorithm. 
Method  isomorphic 
Checks whether the graph is isomorphic to another graph, using the VF2 isomorphism algorithm. 
Method 

Generates a kregular random graph 
Method 

Generates a Kautz graph with parameters (m, n) 
Method  knn 
Calculates the average degree of the neighbors for each vertex, and the same quantity as the function of vertex degree. 
Method  laplacian 
Returns the Laplacian matrix of a graph. 
Method  largest 
Returns the largest cliques of the graph as a list of tuples. 
Method  largest 
Returns the largest independent vertex sets of the graph as a list of tuples. 
Method 

Generates a regular lattice. 
Method  layout 
Place the vertices of a bipartite graph in two layers. 
Method  layout 
Places the vertices of the graph uniformly on a circle or a sphere. 
Method  layout 
Places the vertices on a 2D plane according to the DavidsonHarel layout algorithm. 
Method  layout 
Places the vertices on a 2D plane or in the 3D space ccording to the DrL layout algorithm. 
Method  layout 
Places the vertices on a 2D plane according to the FruchtermanReingold algorithm. 
Method  layout 
This is a port of the graphopt layout algorithm by Michael Schmuhl. graphopt version 0.4.1 was rewritten in C and the support for layers was removed. 
Method  layout 
Places the vertices of a graph in a 2D or 3D grid. 
Method  layout 
Places the vertices on a plane according to the KamadaKawai algorithm. 
Method  layout 
Places the vertices on a 2D plane according to the Large Graph Layout. 
Method  layout 
Places the vertices in an Euclidean space with the given number of dimensions using multidimensional scaling. 
Method  layout 
Places the vertices of the graph randomly. 
Method  layout 
Places the vertices on a 2D plane according to the ReingoldTilford layout algorithm. 
Method  layout 
Circular ReingoldTilford layout for trees. 
Method  layout 
Calculates a starlike layout for the graph. 
Method  LCF 
Generates a graph from LCF notation. 
Method  linegraph 
Returns the line graph of the graph. 
Method  maxdegree 
Returns the maximum degree of a vertex set in the graph. 
Method  maxflow 
Returns the value of the maximum flow between the source and target vertices. 
Method  maximal 
Returns the maximal cliques of the graph as a list of tuples. 
Method  maximal 
Returns the maximal independent vertex sets of the graph as a list of tuples. 
Method  mincut 
Returns the minimum cut between the source and target vertices or within the whole graph. 
Method  minimum 
Returns a list containing all separator vertex sets of minimum size. 
Method  motifs 
Counts the number of motifs in the graph 
Method  motifs 
Counts the total number of motifs in the graph 
Method  motifs 
Counts the total number of motifs in the graph 
Method  neighborhood 
For each vertex specified by vertices, returns the vertices reachable from that vertex in at most order steps. If mindist is larger than zero, vertices that are reachable in less than mindist steps are excluded. 
Method  neighborhood 
For each vertex specified by vertices, returns the number of vertices reachable from that vertex in at most order steps. If mindist is larger than zero, vertices that are reachable in less than mindist... 
Method  neighbors 
Returns adjacent vertices to a given vertex. 
Method  permute 
Permutes the vertices of the graph according to the given permutation and returns the new graph. 
Method  personalized 
Calculates the personalized PageRank values of a graph. 
Method  predecessors 
Returns the predecessors of a given vertex. 
Method 

Generates a graph based on vertex types and connection probabilities. 
Method  radius 
Calculates the radius of the graph. 
Method  random 
Performs a random walk of a given length from a given node. 
Method 

Reads an UCINET DL file and creates a graph based on it. 
Method 

Reads an edge list from a file and creates a graph based on it. 
Method 

Reads a GML file and creates a graph based on it. 
Method 

Reads a GraphDB format file and creates a graph based on it. 
Method 

Reads a GraphML format file and creates a graph based on it. 
Method 

Reads an .lgl file used by LGL. 
Method 

Reads an .ncol file used by LGL. 
Method 

Reads a Pajek format file and creates a graph based on it. 
Method 

Generates a graph from a degree sequence. 
Method 

Generates a graph based on a stochastic model where the probability of an edge gaining a new node is proportional to the edges gained in a given time window. 
Method  reciprocity 
Reciprocity defines the proportion of mutual connections in a directed graph. It is most commonly defined as the probability that the opposite counterpart of a directed edge is also included in the graph... 
Method  rewire 
Randomly rewires the graph while preserving the degree distribution. 
Method  rewire 
Rewires the edges of a graph with constant probability. 
Method 

Generates a ring graph. 
Method  SBM 
Generates a graph based on a stochastic blockmodel. 
Method  shortest 
Calculates shortest path lengths for given vertices in a graph. 
Method  similarity 
Dice similarity coefficient of vertices. 
Method  similarity 
Inverse logweighted similarity coefficient of vertices. 
Method  similarity 
Jaccard similarity coefficient of vertices. 
Method  simplify 
Simplifies a graph by removing selfloops and/or multiple edges. 
Method 

Generates a star graph. 
Method 

Generates a nongrowing graph with edge probabilities proportional to node fitnesses. 
Method 

Generates a nongrowing graph with prescribed powerlaw degree distributions. 
Method  strength 
Returns the strength (weighted degree) of some vertices from the graph 
Method  subcomponent 
Determines the indices of vertices which are in the same component as a given vertex. 
Method  subgraph 
Returns a subgraph spanned by the given edges. 
Method  subisomorphic 
Checks whether a subgraph of the graph is isomorphic to another graph. 
Method  subisomorphic 
Checks whether a subgraph of the graph is isomorphic to another graph. 
Method  successors 
Returns the successors of a given vertex. 
Method  to 
Converts an undirected graph to directed. 
Method  to 
Converts a tree graph into a Prufer sequence. 
Method  to 
Converts a directed graph to undirected. 
Method  topological 
Calculates a possible topological sorting of the graph. 
Method  transitivity 
Calculates the local transitivity (clustering coefficient) of the given vertices in the graph. 
Method  transitivity 
Calculates the global transitivity (clustering coefficient) of the graph. 
Method 

Generates a tree in which almost all vertices have the same number of children. 
Method 

Generates a random tree by sampling uniformly from the set of labelled trees with a given number of nodes. 
Method  unfold 
Unfolds the graph using a BFS to a tree by duplicating vertices as necessary. 
Method  vcount 
Counts the number of vertices. 
Method  vertex 
No summary 
Method  vertex 
Calculates the vertex connectivity of the graph or between some vertices. 
Method 

No summary 
Method  write 
Writes the graph in DOT format to the given file. 
Method  write 
Writes the edge list of a graph to a file. 
Method  write 
Writes the graph in GML format to the given file. 
Method  write 
Writes the graph to a GraphML file. 
Method  write 
Writes the graph to a file in LEDA native format. 
Method  write 
Writes the edge list of a graph to a file in .lgl format. 
Method  write 
Writes the edge list of a graph to a file in .ncol format. 
Method  write 
Writes the graph in Pajek format to the given file. 
Method  __graph 
__graph_as_capsule() 
Method  __register 
Registers a destructor to be called when the object is freed by Python. This function should not be used directly by igraph users. 
Method  _ 
Internal function, undocumented. 
Method  _ 
Internal function, undocumented. 
Method  _get 
Internal function, undocumented. 
Method  _GRG 
Internal function, undocumented. 
Method  _ 
Internal function, undocumented. 
Method  _is 
Internal function, undocumented. 
Method  _is 
Internal function, undocumented. 
Method  _layout 
Internal function, undocumented. 
Method  _maximum 
Internal function, undocumented. 
Method  _ 
Internal function, undocumented. 
Method  _raw 
Returns the memory address of the igraph graph encapsulated by the Python object as an ordinary Python integer. 
Method  _spanning 
Internal function, undocumented. 
igraph._igraph.GraphBase.Adjacency
Generates a graph from its adjacency matrix.
Parameters  
matrix  the adjacency matrix. Possible types are:

mode  the mode to be used. Possible values are:

*args  Undocumented 
**kwargs  Undocumented 
Creates a bipartite graph with the given vertex types and edges. This is similar to the default constructor of the graph, the only difference is that it checks whether all the edges go between the two vertex classes and it assigns the type vector to a type attribute afterwards.
Examples:
>>> g = Graph.Bipartite([0, 1, 0, 1], [(0, 1), (2, 3), (0, 3)]) >>> g.is_bipartite() True >>> g.vs["type"] [False, True, False, True]
Parameters  
types  the vertex types as a boolean list. Anything that evaluates to False will denote a vertex of the first kind, anything that evaluates to True will denote a vertex of the second kind. 
edges  the edges as a list of tuples. 
directed  whether to create a directed graph. Bipartite networks are usually undirected, so the default is False 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the graph with a binary vertex attribute named "type" that stores the vertex classes. 
Generates a graph from one or two dataframes.
Parameters  
edges  pandas DataFrame containing edges and metadata. The first two columns of this DataFrame contain the source and target vertices for each edge. These indicate the vertex *names* rather than ids unless `use_vids` is True and these are nonnegative integers. 
directed  bool setting whether the graph is directed 
vertices  None (default) or pandas DataFrame containing vertex metadata. The first column must contain the unique ids of the vertices and will be set as attribute 'name'. Although vertex names are usually strings, they can be any hashable object. All other columns will be added as vertex attributes by column name. 
use  Undocumented 
Returns  
the graph Vertex names in either the `edges` or `vertices` arguments that are set to NaN (not a number) will be set to the string "NA". That might lead to unexpected behaviour: fill your NaNs with values before calling this function to mitigate.  
Unknown Field: use_vids  
whether to interpret the first two columns of the `edges` argument as vertex ids (0based integers) instead of vertex names. If this argument is set to True and the first two columns of `edges` are not integers, an error is thrown. 
def DictList(cls, vertices, edges, directed=False, vertex_name_attr='name', edge_foreign_keys=(
Constructs a graph from a listofdictionaries representation.
This representation assumes that vertices and edges are encoded in two lists, each list containing a Python dict for each vertex and each edge, respectively. A distinguished element of the vertex dicts contain a vertex ID which is used in the edge dicts to refer to source and target vertices. All the remaining elements of the dict are considered vertex and edge attributes. Note that the implementation does not assume that the objects passed to this method are indeed lists of dicts, but they should be iterable and they should yield objects that behave as dicts. So, for instance, a database query result is likely to be fit as long as it's iterable and yields dictlike objects with every iteration.
Parameters  
vertices  the data source for the vertices or None if there are no special attributes assigned to vertices and we should simply use the edge list of dicts to infer vertex names. 
edges  the data source for the edges. 
directed  whether the constructed graph will be directed 
vertex  the name of the distinguished key in the dicts in the vertex data source that contains the vertex names. Ignored if vertices is None. 
edge  the name of the attributes in the dicts in the edge data source that contain the source and target vertex names. 
iterative  whether to add the edges to the graph one by one, iteratively, or to build a large edge list first and use that to construct the graph. The latter approach is faster but it may not be suitable if your dataset is large. The default is to add the edges in a batch from an edge list. 
Returns  
the graph that was constructed 
Converts the graph from networkx
Vertex names will be converted to "_nx_name" attribute and the vertices will get new ids from 0 up (as standard in igraph).
Parameters  
g  networkx Graph or DiGraph 
Generates a full bipartite graph (directed or undirected, with or without loops).
>>> g = Graph.Full_Bipartite(2, 3) >>> g.is_bipartite() True >>> g.vs["type"] [False, False, True, True, True]
Parameters  
n1  the number of vertices of the first kind. 
n2  the number of vertices of the second kind. 
directed  whether tp generate a directed graph. 
mode  if "out", then all vertices of the first kind are connected to the others; "in" specifies the opposite direction, "all" creates mutual edges. Ignored for undirected graphs. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the graph with a binary vertex attribute named "type" that stores the vertex classes. 
Generates a random geometric graph.
The algorithm drops the vertices randomly on the 2D unit square and connects them if they are closer to each other than the given radius. The coordinates of the vertices are stored in the vertex attributes x and y.
Parameters  
n  The number of vertices in the graph 
radius  The given radius 
torus  This should be True if we want to use a torus instead of a square. 
def Incidence(cls, matrix, directed=False, mode='out', multiple=False, weighted=None, *args, **kwds): ¶
Creates a bipartite graph from an incidence matrix.
Example:
>>> g = Graph.Incidence([[0, 1, 1], [1, 1, 0]])
Parameters  
matrix  the incidence matrix. 
directed  whether to create a directed graph. 
mode  defines the direction of edges in the graph. If "out", then edges go from vertices of the first kind (corresponding to rows of the matrix) to vertices of the second kind (the columns of the matrix). If "in", the opposite direction is used. "all" creates mutual edges. Ignored for undirected graphs. 
multiple  defines what to do with nonzero entries in the matrix. If False, nonzero entries will create an edge no matter what the value is. If True, nonzero entries are rounded up to the nearest integer and this will be the number of multiple edges created. 
weighted  defines whether to create a weighted graph from the incidence matrix. If it is c{None} then an unweighted graph is created and the multiple argument is used to determine the edges of the graph. If it is a string then for every nonzero matrix entry, an edge is created and the value of the entry is added as an edge attribute named by the weighted argument. If it is True then a weighted graph is created and the name of the edge attribute will be ‘weight’. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the graph with a binary vertex attribute named "type" that stores the vertex classes.  
Raises  
ValueError  if the weighted and multiple are passed together. 
def Random_Bipartite(cls, n1, n2, p=None, m=None, directed=False, neimode='all', *args, **kwds): ¶
Generates a random bipartite graph with the given number of vertices and edges (if m is given), or with the given number of vertices and the given connection probability (if p is given).
If m is given but p is not, the generated graph will have n1 vertices of type 1, n2 vertices of type 2 and m randomly selected edges between them. If p is given but m is not, the generated graph will have n1 vertices of type 1 and n2 vertices of type 2, and each edge will exist between them with probability p.
Parameters  
n1  the number of vertices of type 1. 
n2  the number of vertices of type 2. 
p  the probability of edges. If given, m must be missing. 
m  the number of edges. If given, p must be missing. 
directed  whether to generate a directed graph. 
neimode  if the graph is directed, specifies how the edges will be generated. If it is "all", edges will be generated in both directions (from type 1 to type 2 and vice versa) independently. If it is "out" edges will always point from type 1 to type 2. If it is "in", edges will always point from type 2 to type 1. This argument is ignored for undirected graphs. 
*args  Undocumented 
**kwds  Undocumented 
Unified reading function for graphs.
This method tries to identify the format of the graph given in the first parameter and calls the corresponding reader method.
The remaining arguments are passed to the reader method without any changes.
Parameters  
f  the file containing the graph to be loaded 
format  the format of the file (if known in advance). None means autodetection. Possible values are: "ncol" (NCOL format), "lgl" (LGL format), "graphdb" (GraphDB format), "graphml", "graphmlz" (GraphML and gzipped GraphML format), "gml" (GML format), "net", "pajek" (Pajek format), "dimacs" (DIMACS format), "edgelist", "edges" or "edge" (edge list), "adjacency" (adjacency matrix), "dl" (DL format used by UCINET), "pickle" (Python pickled format), "picklez" (gzipped Python pickled format) 
*args  Undocumented 
**kwds  Undocumented 
Raises  
IOError  if the file format can't be identified and none was given. 
def Read_Adjacency(cls, f, sep=None, comment_char='#', attribute=None, *args, **kwds): ¶
Constructs a graph based on an adjacency matrix from the given file.
Additional positional and keyword arguments not mentioned here are passed intact to Adjacency
.
Parameters  
f  the name of the file to be read or a file object 
sep  the string that separates the matrix elements in a row. None means an arbitrary sequence of whitespace characters. 
comment  lines starting with this string are treated as comments. 
attribute  an edge attribute name where the edge weights are stored in the case of a weighted adjacency matrix. If None, no weights are stored, values larger than 1 are considered as edge multiplicities. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the created graph 
igraph._igraph.GraphBase.Read_DIMACS
Reads a graph from a file conforming to the DIMACS minimumcost flow file format.
For the exact definition of the format, see http://lpsolve.sourceforge.net/5.5/DIMACS.htm.
Restrictions compared to the official description of the format are as follows:
 igraph's DIMACS reader requires only three fields in an arc definition, describing the edge's source and target node and its capacity.
 Source vertices are identified by 's' in the FLOW field, target vertices are identified by 't'.
 Node indices start from 1. Only a single source and target node is allowed.
Parameters  
f  the name of the file or a Python file handle 
directed  whether the generated graph should be directed. 
Returns  
the generated graph. The indices of the source and target vertices are attached as graph attributes source and target, the edge capacities are stored in the capacity edge attribute. 
Reads a graph from a zipped GraphML file.
Parameters  
f  the name of the file 
directed  Undocumented 
index  if the GraphML file contains multiple graphs, specified the one that should be loaded. Graph indices start from zero, so if you want to load the first graph, specify 0 here. 
Returns  
the loaded graph object 
Reads a graph from Python pickled format
Parameters  
fname  the name of the file, a stream to read from, or a string containing the pickled data. 
Returns  
the created graph object. 
Reads a graph from compressed Python pickled format, uncompressing it onthefly.
Parameters  
fname  the name of the file or a stream to read from. 
Returns  
the created graph object. 
def TupleList(cls, edges, directed=False, vertex_name_attr='name', edge_attrs=None, weights=False): ¶
Constructs a graph from a listoftuples representation.
This representation assumes that the edges of the graph are encoded in a list of tuples (or lists). Each item in the list must have at least two elements, which specify the source and the target vertices of the edge. The remaining elements (if any) specify the edge attributes of that edge, where the names of the edge attributes originate from the edge_attrs list. The names of the vertices will be stored in the vertex attribute given by vertex_name_attr.
The default parameters of this function are suitable for creating unweighted graphs from lists where each item contains the source vertex and the target vertex. If you have a weighted graph, you can use items where the third item contains the weight of the edge by setting edge_attrs to "weight" or ["weight"]. If you have even more edge attributes, add them to the end of each item in the edges list and also specify the corresponding edge attribute names in edge_attrs as a list.
Parameters  
edges  the data source for the edges. This must be a list where each item is a tuple (or list) containing at least two items: the name of the source and the target vertex. Note that names will be assigned to the name vertex attribute (or another vertex attribute if vertex_name_attr is specified), even if all the vertex names in the list are in fact numbers. 
directed  whether the constructed graph will be directed 
vertex  the name of the vertex attribute that will contain the vertex names. 
edge  the names of the edge attributes that are filled with the extra items in the edge list (starting from index 2, since the first two items are the source and target vertices). None means that only the source and target vertices will be extracted from each item. If you pass a string here, it will be wrapped in a list for convenience. 
weights  alternative way to specify that the graph is weighted. If you set weights to true and edge_attrs is not given, it will be assumed that edge_attrs is ["weight"] and igraph will parse the third element from each item into an edge weight. If you set weights to a string, it will be assumed that edge_attrs contains that string only, and igraph will store the edge weights in that attribute. 
Returns  
the graph that was constructed 
Generates a graph from its weighted adjacency matrix.
Parameters  
matrix  the adjacency matrix. Possible types are:

mode  the mode to be used. Possible values are:
These values can also be given as strings without the ADJ prefix. 
attr  the name of the edge attribute that stores the edge weights. 
loops  whether to include loop edges. When False, the diagonal of the adjacency matrix will be ignored. 
Copies the graph and extends the copy depending on the type of the other object given.
Parameters  
other  if it is an integer, the copy is extended by the given number of vertices. If it is a string, the copy is extended by a single vertex whose name attribute will be equal to the given string. If it is a tuple with two elements, the copy is extended by a single edge. If it is a list of tuples, the copy is extended by multiple edges. If it is a Graph , a disjoint union is performed. 
Graph intersection operator.
Parameters  
other  the other graph to take the intersection with. 
Returns  
the intersected graph. 
Coercion rules.
This method is needed to allow the graph to react to additions with lists, tuples, integers, strings, vertices, edges and so on.
__init__(n=0, edges=None, directed=False, graph_attrs=None, vertex_attrs=None, edge_attrs=None)
Constructs a graph from scratch.
Parameters  
*args  Undocumented 
**kwds  Undocumented 
n  the number of vertices. Can be omitted, the default is zero. Note that if the edge list contains vertices with indexes larger than or equal to m, then the number of vertices will be adjusted accordingly. 
edges  the edge list where every list item is a pair of integers. If any of the integers is larger than n − 1, the number of vertices is adjusted accordingly. None means no edges. 
directed  whether the graph should be directed 
graph  the attributes of the graph as a dictionary. 
vertex  the attributes of the vertices as a dictionary. Every dictionary value must be an iterable with exactly n items. 
edge  the attributes of the edges as a dictionary. Every dictionary value must be an iterable with exactly m items where m is the number of edges. 
Copies exact replicas of the original graph an arbitrary number of times.
Parameters  
other  if it is an integer, multiplies the graph by creating the given number of identical copies and taking the disjoint union of them. 
Plots the graph to the given Cairo context in the given bounding box
The visual style of vertices and edges can be modified at three places in the following order of precedence (lower indices override higher indices):
 Keyword arguments of this function (or of
plot()
which is passed intact to Graph.__plot__().  Vertex or edge attributes, specified later in the list of keyword arguments.
 igraphwide plotting defaults (see
igraph.config.Configuration
)  Builtin defaults.
E.g., if the vertex_size keyword attribute is not present, but there exists a vertex attribute named size, the sizes of the vertices will be specified by that attribute.
Besides the usual selfexplanatory plotting parameters (context, bbox, palette), it accepts the following keyword arguments:
autocurve: whether to use curves instead of straight lines for multiple edges on the graph plot. This argument may be True or False; when omitted, True is assumed for graphs with less than 10.000 edges and False otherwise.
drawer_factory: a subclass of
AbstractCairoGraphDrawer
which will be used to draw the graph. You may also provide a function here which takes two arguments: the Cairo context to draw on and a bounding box (an instance ofBoundingBox
). If this keyword argument is missing, igraph will use the default graph drawer which should be suitable for most purposes. It is safe to omit this keyword argument unless you need to use a specific graph drawer.keep_aspect_ratio: whether to keep the aspect ratio of the layout that igraph calculates to place the nodes. True means that the layout will be scaled proportionally to fit into the bounding box where the graph is to be drawn but the aspect ratio will be kept the same (potentially leaving empty space next to, below or above the graph). False means that the layout will be scaled independently along the X and Y axis in order to fill the entire bounding box. The default is False.
layout: the layout to be used. If not an instance of
Layout
, it will be passed tolayout
to calculate the layout. Note that if you want a deterministic layout that does not change with every plot, you must either use a deterministic layout function (likelayout_circle
) or calculate the layout in advance and pass aLayout
object here.margin: the top, right, bottom, left margins as a 4tuple. If it has less than 4 elements or is a single float, the elements will be reused until the length is at least 4.
mark_groups: whether to highlight some of the vertex groups by colored polygons. This argument can be one of the following:
 False: no groups will be highlighted
 True: only valid if the object plotted is a
VertexClustering
orVertexCover
. The vertex groups in the clutering or cover will be highlighted such that the ith group will be colored by the ith color from the current palette. If used when plotting a graph, it will throw an error.  A dict mapping tuples of vertex indices to color names. The given vertex groups will be highlighted by the given colors.
 A list containing pairs or an iterable yielding pairs, where the first element of each pair is a list of vertex indices and the second element is a color.
 A
VertexClustering
orVertexCover
instance. The vertex groups in the clustering or cover will be highlighted such that the ith group will be colored by the ith color from the current palette.
In place of lists of vertex indices, you may also use
VertexSeq
instances.In place of color names, you may also use color indices into the current palette. None as a color name will mean that the corresponding group is ignored.
vertex_size: size of the vertices. The corresponding vertex attribute is called size. The default is 10. Vertex sizes are measured in the unit of the Cairo context on which igraph is drawing.
vertex_color: color of the vertices. The corresponding vertex attribute is color, the default is red. Colors can be specified either by common X11 color names (see the source code of
igraph.drawing.colors
for a list of known colors), by 3tuples of floats (ranging between 0 and 255 for the R, G and B components), by CSSstyle string specifications (#rrggbb) or by integer color indices of the specified palette.vertex_frame_color: color of the frame (i.e. stroke) of the vertices. The corresponding vertex attribute is frame_color, the default is black. See vertex_color for the possible ways of specifying a color.
vertex_frame_width: the width of the frame (i.e. stroke) of the vertices. The corresponding vertex attribute is frame_width. The default is 1. Vertex frame widths are measured in the unit of the Cairo context on which igraph is drawing.
vertex_shape: shape of the vertices. Alternatively it can be specified by the shape vertex attribute. Possibilities are: square, {circle}, {triangle}, {triangledown} or hidden. See the source code of
igraph.drawing
for a list of alternative shape names that are also accepted and mapped to these.vertex_label: labels drawn next to the vertices. The corresponding vertex attribute is label.
vertex_label_dist: distance of the midpoint of the vertex label from the center of the corresponding vertex. The corresponding vertex attribute is label_dist.
vertex_label_color: color of the label. Corresponding vertex attribute: label_color. See vertex_color for color specification syntax.
vertex_label_size: font size of the label, specified in the unit of the Cairo context on which we are drawing. Corresponding vertex attribute: label_size.
vertex_label_angle: the direction of the line connecting the midpoint of the vertex with the midpoint of the label. This can be used to position the labels relative to the vertices themselves in conjunction with vertex_label_dist. Corresponding vertex attribute: label_angle. The default is math.pi/2.
vertex_order: drawing order of the vertices. This must be a list or tuple containing vertex indices; vertices are then drawn according to this order.
vertex_order_by: an alternative way to specify the drawing order of the vertices; this attribute is interpreted as the name of a vertex attribute, and vertices are drawn such that those with a smaller attribute value are drawn first. You may also reverse the order by passing a tuple here; the first element of the tuple should be the name of the attribute, the second element specifies whether the order is reversed (True, False, "asc" and "desc" are accepted values).
edge_color: color of the edges. The corresponding edge attribute is color, the default is red. See vertex_color for color specification syntax.
edge_curved: whether the edges should be curved. Positive numbers correspond to edges curved in a counterclockwise direction, negative numbers correspond to edges curved in a clockwise direction. Zero represents straight edges. True is interpreted as 0.5, False is interpreted as 0. The default is 0 which makes all the edges straight.
edge_width: width of the edges in the default unit of the Cairo context on which we are drawing. The corresponding edge attribute is width, the default is 1.
edge_arrow_size: arrow size of the edges. The corresponding edge attribute is arrow_size, the default is 1.
edge_arrow_width: width of the arrowhead on the edge. The corresponding edge attribute is arrow_width, the default is 1.
edge_order: drawing order of the edges. This must be a list or tuple containing edge indices; edges are then drawn according to this order.
edge_order_by: an alternative way to specify the drawing order of the edges; this attribute is interpreted as the name of an edge attribute, and edges are drawn such that those with a smaller attribute value are drawn first. You may also reverse the order by passing a tuple here; the first element of the tuple should be the name of the attribute, the second element specifies whether the order is reversed (True, False, "asc" and "desc" are accepted values).
Returns a string representation of the graph.
Behind the scenes, this method constructs a GraphSummary
instance and invokes its __str__ method with a verbosity of 1 and attribute printing turned off.
See the documentation of GraphSummary
for more details about the output.
Removes the given object(s) from the graph
Parameters  
other  if it is an integer, removes the vertex with the given ID from the graph (note that the remaining vertices will get reindexed!). If it is a tuple, removes the given edge. If it is a graph, takes the difference of the two graphs. Accepts lists of integers or lists of tuples as well, but they can't be mixed! Also accepts Edge and EdgeSeq objects. 
Adds a single edge to the graph.
Keyword arguments (except the source and target arguments) will be assigned to the edge as attributes.
The performance cost of adding a single edge or several edges to a graph is similar. Thus, when adding several edges, a single add_edges() call is more efficient than multiple add_edge() calls.
Parameters  
source  the source vertex of the edge or its name. 
target  the target vertex of the edge or its name. 
**kwds  Undocumented 
Returns  
the newly added edge as an Edge object. Use add_edges([(source, target)]) if you don't need the Edge object and want to avoid the overhead of creating it. 
igraph._igraph.GraphBase.add_edges
Adds some edges to the graph.
Parameters  
es  the list of edges to be added. Every edge is represented with a tuple containing the vertex IDs or names of the two endpoints. Vertices are enumerated from zero. 
attributes  dict of sequences, all of length equal to the number of edges to be added, containing the attributes of the new edges. 
Adds a single vertex to the graph. Keyword arguments will be assigned as vertex attributes. Note that name as a keyword argument is treated specially; if a graph has name as a vertex attribute, it allows one to refer to vertices by their names in most places where igraph expects a vertex ID.
Returns  
the newly added vertex as a Vertex object. Use add_vertices(1) if you don't need the Vertex object and want to avoid the overhead of creating t. 
igraph._igraph.GraphBase.add_vertices
Adds some vertices to the graph.
Note that if n is a sequence of strings, indicating the names of the new vertices, and attributes has a key name, the two conflict. In that case the attribute will be applied.
Parameters  
n  the number of vertices to be added, or the name of a single vertex to be added, or a sequence of strings, each corresponding to the name of a vertex to be added. Names will be assigned to the name vertex attribute. 
attributes  dict of sequences, all of length equal to the number of vertices to be added, containing the attributes of the new vertices. If n is a string (so a single vertex is added), then the values of this dict are the attributes themselves, but if n=1 then they have to be lists of length 1. 
igraph._igraph.GraphBase.all_st_cuts
Returns all the cuts between the source and target vertices in a directed graph.
This function lists all edgecuts between a source and a target vertex. Every cut is listed exactly once.
Parameters  
source  the source vertex ID 
target  the target vertex ID 
Returns  
a list of Cut objects.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
JS Provan and DR Shier: A paradigm for listing (s,t)cuts in graphs. Algorithmica 15, 351372, 1996. 
igraph._igraph.GraphBase.all_st_mincuts
Returns all the mincuts between the source and target vertices in a directed graph.
This function lists all minimum edgecuts between a source and a target vertex.
Parameters  
source  the source vertex ID 
target  the target vertex ID 
capacity  the edge capacities (weights). If None, all edges have equal weight. May also be an attribute name. 
Returns  
a list of Cut objects.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
JS Provan and DR Shier: A paradigm for listing (s,t)cuts in graphs. Algorithmica 15, 351372, 1996. 
Returns a directed copy of this graph. Arguments are passed on to to_directed()
that is invoked on the copy.
Returns an undirected copy of this graph. Arguments are passed on to to_undirected()
that is invoked on the copy.
Calculates the biconnected components of the graph.
Parameters  
return  whether to return the articulation points as well 
Returns  
a VertexCover object describing the biconnected components, and optionally the list of articulation points as well 
Projects a bipartite graph into two onemode graphs. Edge directions are ignored while projecting.
Examples:
>>> g = Graph.Full_Bipartite(10, 5) >>> g1, g2 = g.bipartite_projection() >>> g1.isomorphic(Graph.Full(10)) True >>> g2.isomorphic(Graph.Full(5)) True
Parameters  
types  an igraph vector containing the vertex types, or an attribute name. Anything that evalulates to False corresponds to vertices of the first kind, everything else to the second kind. 
multiplicity  if True, then igraph keeps the multiplicity of the edges in the projection in an edge attribute called "weight". E.g., if there is an ACB and an ADB triplet in the bipartite graph and there is no other X (apart from X=B and X=D) for which an AXB triplet would exist in the bipartite graph, the multiplicity of the AB edge in the projection will be 2. 
probe1  this argument can be used to specify the order of the projections in the resulting list. If given and nonnegative, then it is considered as a vertex ID; the projection containing the vertex will be the first one in the result. 
which  this argument can be used to specify which of the two projections should be returned if only one of them is needed. Passing 0 here means that only the first projection is returned, while 1 means that only the second projection is returned. (Note that we use 0 and 1 because Python indexing is zerobased). False is equivalent to 0 and True is equivalent to 1. Any other value means that both projections will be returned in a tuple. 
Returns  
a tuple containing the two projected onemode graphs if which is not 1 or 2, or the projected onemode graph specified by the which argument if its value is 0, 1, False or True. 
Calculates the number of vertices and edges in the bipartite projections of this graph according to the specified vertex types. This is useful if you have a bipartite graph and you want to estimate the amount of memory you would need to calculate the projections themselves.
Parameters  
types  an igraph vector containing the vertex types, or an attribute name. Anything that evalulates to False corresponds to vertices of the first kind, everything else to the second kind. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
a 4tuple containing the number of vertices and edges in the first projection, followed by the number of vertices and edges in the second projection. 
Clears the graph, deleting all vertices, edges, and attributes.
See Also  
delete_vertices and delete_edges . 
igraph._igraph.GraphBase.clusters
Calculates the (strong or weak) clusters (connected components) for a given graph.
Parameters  
mode  must be either "strong" or "weak", depending on the clusters being sought. Optional, defaults to "strong". 
Returns  
a VertexClustering object 
igraph._igraph.GraphBase.cohesive_blocks
Calculates the cohesive block structure of the graph.
Cohesive blocking is a method of determining hierarchical subsets of graph vertices based on their structural cohesion (i.e. vertex connectivity). For a given graph G, a subset of its vertices S is said to be maximally kcohesive if there is no superset of S with vertex connectivity greater than or equal to k. Cohesive blocking is a process through which, given a kcohesive set of vertices, maximally lcohesive subsets are recursively identified with l > k. Thus a hierarchy of vertex subsets is obtained in the end, with the entire graph G at its root.
Returns  
an instance of CohesiveBlocks . See the documentation of CohesiveBlocks for more information.  
See Also  
CohesiveBlocks 
Community structure based on the betweenness of the edges in the network.
The idea is that the betweenness of the edges connecting two communities is typically high, as many of the shortest paths between nodes in separate communities go through them. So we gradually remove the edge with the highest betweenness and recalculate the betweennesses after every removal. This way sooner or later the network falls of to separate components. The result of the clustering will be represented by a dendrogram.
Parameters  
clusters  the number of clusters we would like to see. This practically defines the "level" where we "cut" the dendrogram to get the membership vector of the vertices. If None, the dendrogram is cut at the level which maximizes the modularity when the graph is unweighted; otherwise the dendrogram is cut at at a single cluster (because cluster count selection based on modularities does not make sense for this method if not all the weights are equal). 
directed  whether the directionality of the edges should be taken into account or not. 
weights  name of an edge attribute or a list containing edge weights. 
Returns  
a VertexDendrogram object, initally cut at the maximum modularity or at the desired number of clusters. 
Community structure based on the greedy optimization of modularity.
This algorithm merges individual nodes into communities in a way that greedily maximizes the modularity score of the graph. It can be proven that if no merge can increase the current modularity score, the algorithm can be stopped since no further increase can be achieved.
This algorithm is said to run almost in linear time on sparse graphs.
Parameters  
weights  edge attribute name or a list containing edge weights 
Returns  
an appropriate VertexDendrogram object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
A Clauset, MEJ Newman and C Moore: Finding community structure in very large networks. Phys Rev E 70, 066111 (2004). 
Finds the community structure of the network according to the Infomap method of Martin Rosvall and Carl T. Bergstrom.
Parameters  
edge  name of an edge attribute or a list containing edge weights. 
vertex  name of an vertex attribute or a list containing vertex weights. 
trials  the number of attempts to partition the network. 
Returns  
an appropriate VertexClustering object with an extra attribute called codelength that stores the code length determined by the algorithm.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
M. Rosvall and C. T. Bergstrom: Maps of information flow reveal community structure in complex networks, PNAS 105, 1118 (2008). http://dx.doi.org/10.1073/pnas.0706851105, http://arxiv.org/abs/0707.0609.  
M. Rosvall, D. Axelsson, and C. T. Bergstrom: The map equation, Eur. Phys. J. Special Topics 178, 13 (2009). http://dx.doi.org/10.1140/epjst/e2010011791, http://arxiv.org/abs/0906.1405. 
Finds the community structure of the graph according to the label propagation method of Raghavan et al.
Initially, each vertex is assigned a different label. After that, each vertex chooses the dominant label in its neighbourhood in each iteration. Ties are broken randomly and the order in which the vertices are updated is randomized before every iteration. The algorithm ends when vertices reach a consensus. Note that since ties are broken randomly, there is no guarantee that the algorithm returns the same community structure after each run. In fact, they frequently differ. See the paper of Raghavan et al on how to come up with an aggregated community structure.
Parameters  
weights  name of an edge attribute or a list containing edge weights 
initial  name of a vertex attribute or a list containing the initial vertex labels. Labels are identified by integers from zero to n − 1 where n is the number of vertices. Negative numbers may also be present in this vector, they represent unlabeled vertices. 
fixed  a list of booleans for each vertex. True corresponds to vertices whose labeling should not change during the algorithm. It only makes sense if initial labels are also given. Unlabeled vertices cannot be fixed. It may also be the name of a vertex attribute; each attribute value will be interpreted as a Boolean. 
Returns  
an appropriate VertexClustering object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Raghavan, U.N. and Albert, R. and Kumara, S. Near linear time algorithm to detect community structures in largescale networks. Phys Rev E 76:036106, 2007. http://arxiv.org/abs/0709.2938. 
Newman's leading eigenvector method for detecting community structure.
This is the proper implementation of the recursive, divisive algorithm: each split is done by maximizing the modularity regarding the original network.
Parameters  
clusters  the desired number of communities. If None, the algorithm tries to do as many splits as possible. Note that the algorithm won't split a community further if the signs of the leading eigenvector are all the same, so the actual number of discovered communities can be less than the desired one. 
weights  name of an edge attribute or a list containing edge weights. 
arpack  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used. 
Returns  
an appropriate VertexClustering object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
MEJ Newman: Finding community structure in networks using the eigenvectors of matrices, arXiv:physics/0605087 
Naive implementation of Newman's eigenvector community structure detection.
This function splits the network into two components according to the leading eigenvector of the modularity matrix and then recursively takes the given number of steps by splitting the communities as individual networks. This is not the correct way, however, see the reference for explanation. Consider using the correct community_leading_eigenvector
method instead.
Parameters  
clusters  the desired number of communities. If None, the algorithm tries to do as many splits as possible. Note that the algorithm won't split a community further if the signs of the leading eigenvector are all the same, so the actual number of discovered communities can be less than the desired one. 
return  whether the returned object should be a dendrogram instead of a single clustering. 
Returns  
an appropriate VertexClustering or VertexDendrogram object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
MEJ Newman: Finding community structure in networks using the eigenvectors of matrices, arXiv:physics/0605087 
Finds the community structure of the graph using the Leiden algorithm of Traag, van Eck & Waltman.
Parameters  
objective  whether to use the Constant Potts Model (CPM) or modularity. Must be either "CPM" or "modularity". 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
resolution  the resolution parameter to use. Higher resolutions lead to more smaller communities, while lower resolutions lead to fewer larger communities. 
beta  parameter affecting the randomness in the Leiden algorithm. This affects only the refinement step of the algorithm. 
initial  if provided, the Leiden algorithm will try to improve this provided membership. If no argument is provided, the aglorithm simply starts from the singleton partition. 
n  the number of iterations to iterate the Leiden algorithm. Each iteration may improve the partition further. Using a negative number of iterations will run until a stable iteration is encountered (i.e. the quality was not increased during that iteration). 
node  the node weights used in the Leiden algorithm. If this is not provided, it will be automatically determined on the basis of whether you want to use CPM or modularity. If you do provide this, please make sure that you understand what you are doing. 
Returns  
an appropriate VertexClustering object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Traag, V. A., Waltman, L., & van Eck, N. J. (2019). From Louvain to Leiden: guaranteeing wellconnected communities. Scientific reports, 9(1), 5233. doi: 10.1038/s4159801941695z 
Community structure based on the multilevel algorithm of Blondel et al.
This is a bottomup algorithm: initially every vertex belongs to a separate community, and vertices are moved between communities iteratively in a way that maximizes the vertices' local contribution to the overall modularity score. When a consensus is reached (i.e. no single move would increase the modularity score), every community in the original graph is shrank to a single vertex (while keeping the total weight of the adjacent edges) and the process continues on the next level. The algorithm stops when it is not possible to increase the modularity any more after shrinking the communities to vertices.
This algorithm is said to run almost in linear time on sparse graphs.
Parameters  
weights  edge attribute name or a list containing edge weights 
return  if True, the communities at each level are returned in a list. If False, only the community structure with the best modularity is returned. 
Returns  
a list of VertexClustering objects, one corresponding to each level (if return_levels is True), or a VertexClustering corresponding to the best modularity.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
VD Blondel, JL Guillaume, R Lambiotte and E Lefebvre: Fast unfolding of community hierarchies in large networks, J Stat Mech P10008 (2008), http://arxiv.org/abs/0803.0476 
Calculates the optimal modularity score of the graph and the corresponding community structure.
This function uses the GNU Linear Programming Kit to solve a large integer optimization problem in order to find the optimal modularity score and the corresponding community structure, therefore it is unlikely to work for graphs larger than a few (less than a hundred) vertices. Consider using one of the heuristic approaches instead if you have such a large graph.
Returns  
the calculated membership vector and the corresponding modularity in a tuple. 
Finds the community structure of the graph according to the spinglass community detection method of Reichardt & Bornholdt.
Parameters  
*args  Undocumented 
**kwds  Undocumented 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
spins  integer, the number of spins to use. This is the upper limit for the number of communities. It is not a problem to supply a (reasonably) big number here, in which case some spin states will be unpopulated. 
parupdate  whether to update the spins of the vertices in parallel (synchronously) or not 
start  the starting temperature 
stop  the stop temperature 
cool  cooling factor for the simulated annealing 
update  specifies the null model of the simulation. Possible values are "config" (a random graph with the same vertex degrees as the input graph) or "simple" (a random graph with the same number of edges) 
gamma  the gamma argument of the algorithm, specifying the balance between the importance of present and missing edges within a community. The default value of 1.0 assigns equal importance to both of them. 
implementation  currently igraph contains two implementations of the spinglass community detection algorithm. The faster original implementation is the default. The other implementation is able to take into account negative weights, this can be chosen by setting implementation to "neg" 
lambda_  the lambda argument of the algorithm, which specifies the balance between the importance of present and missing negatively weighted edges within a community. Smaller values of lambda lead to communities with less negative intraconnectivity. If the argument is zero, the algorithm reduces to a graph coloring algorithm, using the number of spins as colors. This argument is ignored if the original implementation is used. Note the underscore at the end of the argument name; this is due to the fact that lambda is a reserved keyword in Python. 
Returns  
an appropriate VertexClustering object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Reichardt J and Bornholdt S: Statistical mechanics of community detection. Phys Rev E 74:016110 (2006). http://arxiv.org/abs/condmat/0603718.  
Traag VA and Bruggeman J: Community detection in networks with positive and negative links. Phys Rev E 80:036115 (2009). http://arxiv.org/abs/0811.2329. 
Community detection algorithm of Latapy & Pons, based on random walks.
The basic idea of the algorithm is that short random walks tend to stay in the same community. The result of the clustering will be represented as a dendrogram.
Parameters  
weights  name of an edge attribute or a list containing edge weights 
steps  length of random walks to perform 
Returns  
a VertexDendrogram object, initially cut at the maximum modularity.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Pascal Pons, Matthieu Latapy: Computing communities in large networks using random walks, http://arxiv.org/abs/physics/0512106. 
Returns the number of automorphisms of the graph.
This function simply calls count_isomorphisms_vf2 with the graph itself. See count_isomorphisms_vf2 for an explanation of the parameters.
Returns  
the number of automorphisms of the graph  
See Also  
Graph.count_isomorphisms_vf2 
Calculates the degree distribution of the graph.
Unknown keyword arguments are directly passed to degree()
.
Parameters  
bin  the bin width of the histogram 
*args  Undocumented 
**kwds  Undocumented 
Returns  
a histogram representing the degree distribution of the graph. 
igraph._igraph.GraphBase.delete_edges
Deletes some edges from the graph.
The set of edges to be deleted is determined by the positional and keyword arguments. If the function is called without any arguments, all edges are deleted. If any keyword argument is present, or the first positional argument is callable, an edge sequence is derived by calling EdgeSeq.select
with the same positional and keyword arguments. Edges in the derived edge sequence will be removed. Otherwise the first positional argument is considered as follows:
 None  deletes all edges (deprecated since 0.8.3)
 a single integer  deletes the edge with the given ID
 a list of integers  deletes the edges denoted by the given IDs
 a list of 2tuples  deletes the edges denoted by the given sourcetarget vertex pairs. When multiple edges are present between a given sourcetarget vertex pair, only one is removed.
Unknown Field: deprecated  
delete_edges(None) has been replaced by delete_edges()  with no arguments  since igraph 0.8.3. 
Conducts a depth first search (DFS) on the graph.
Parameters  
vid  the root vertex ID 
mode  either "in" or "out" or "all", ignored for undirected graphs. 
Returns  
a tuple with the following items:

Creates the disjoint union of two (or more) graphs.
Parameters  
other  graph or list of graphs to be united with the current one. 
Returns  
the disjoint union graph 
igraph._igraph.GraphBase.dyad_census
Calculates the dyad census of the graph.
Dyad census means classifying each pair of vertices of a directed graph into three categories: mutual (there is an edge from a to b and also from b to a), asymmetric (there is an edge from a to b or from b to a but not the other way round) and null (there is no connection between a and b).
Returns  
a DyadCensus object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Holland, P.W. and Leinhardt, S. (1970). A Method for Detecting Structure in Sociometric Data. American Journal of Sociology, 70, 492513. 
igraph._igraph.GraphBase.get_adjacency
Returns the adjacency matrix of a graph.
Parameters  
type  either GET_ADJACENCY_LOWER (uses the lower triangle of the matrix) or GET_ADJACENCY_UPPER (uses the upper triangle) or GET_ADJACENCY_BOTH (uses both parts). Ignored for directed graphs. 
attribute  if None, returns the ordinary adjacency matrix. When the name of a valid edge attribute is given here, the matrix returned will contain the default value at the places where there is no edge or the value of the given attribute where there is an edge. Multiple edges are not supported, the value written in the matrix in this case will be unpredictable. This parameter is ignored if eids is True 
default  the default value written to the cells in the case of adjacency matrices with attributes. 
eids  specifies whether the edge IDs should be returned in the adjacency matrix. Since zero is a valid edge ID, the cells in the matrix that correspond to unconnected vertex pairs will contain 1 instead of 0 if eids is True. If eids is False, the number of edges will be returned in the matrix for each vertex pair. 
Returns  
the adjacency matrix as a Matrix . 
Returns the adjacency matrix of a graph as a SciPy CSR matrix.
Parameters  
attribute  if None, returns the ordinary adjacency matrix. When the name of a valid edge attribute is given here, the matrix returned will contain the default value at the places where there is no edge or the value of the given attribute where there is an edge. 
Returns  
the adjacency matrix as a scipy.sparse.csr_matrix. 
Returns the adjacency list representation of the graph.
The adjacency list representation is a list of lists. Each item of the outer list belongs to a single vertex of the graph. The inner list contains the neighbors of the given vertex.
Parameters  
mode  if "out", returns the successors of the vertex. If "in", returns the predecessors of the vertex. If "all"", both the predecessors and the successors will be returned. Ignored for undirected graphs. 
Calculates all the simple paths from a given node to some other nodes (or all of them) in a graph.
A path is simple if its vertices are unique, i.e. no vertex is visited more than once.
Note that potentially there are exponentially many paths between two vertices of a graph, especially if your graph is latticelike. In this case, you may run out of memory when using this function.
Parameters  
v  the source for the calculated paths 
to  a vertex selector describing the destination for the calculated paths. This can be a single vertex ID, a list of vertex IDs, a single vertex name, a list of vertex names or a VertexSeq object. None means all the vertices. 
cutoff  maximum length of path that is considered. If negative, paths of all lengths are considered. 
mode  the directionality of the paths. "in" means to calculate incoming paths, "out" means to calculate outgoing paths, "all" means to calculate both ones. 
Returns  
all of the simple paths from the given node to every other reachable node in the graph in a list. Note that in case of mode="in", the vertices in a path are returned in reversed order! 
Returns all the automorphisms of the graph
This function simply calls get_isomorphisms_vf2 with the graph itself. See get_isomorphisms_vf2 for an explanation of the parameters.
Returns  
a list of lists, each item containing a possible mapping of the graph vertices to itself according to the automorphism  
See Also  
Graph.get_isomorphisms_vf2 
Export edges with attributes to pandas.DataFrame
If you want to use source and target vertex IDs as index, you can do:
>>> from string import ascii_letters >>> graph = Graph.GRG(25, 0.4) >>> graph.vs["name"] = ascii_letters[:graph.vcount()] >>> df = graph.get_edge_dataframe() >>> df.set_index(['source', 'target'], inplace=True)
The index will be a pandas.MultiIndex. You can use the `drop=False` option to keep the `source` and `target` columns.
If you want to use vertex names in the source and target columns:
>>> df = graph.get_edge_dataframe() >>> df_vert = graph.get_vertex_dataframe() >>> df['source'].replace(df_vert['name'], inplace=True) >>> df['target'].replace(df_vert['name'], inplace=True) >>> df_vert.set_index('name', inplace=True) # Optional
Returns  
a pandas.DataFrame representing edges and their attributes. The index uses edge IDs, from 0 to M  1 where M is the number of edges. The first two columns of the dataframe represent the IDs of source and target vertices for each edge. These columns have names "source" and "target". If your edges have attributes with the same names, they will be present in the dataframe, but not in the first two columns. 
igraph._igraph.GraphBase.get_incidence
Returns the incidence matrix of a bipartite graph. The incidence matrix is an n times m matrix, where n and m are the number of vertices in the two vertex classes.
Parameters  
types  an igraph vector containing the vertex types, or an attribute name. Anything that evalulates to False corresponds to vertices of the first kind, everything else to the second kind. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the incidence matrix and two lists in a triplet. The first list defines the mapping between row indices of the matrix and the original vertex IDs. The second list is the same for the column indices. 
Returns the incidence list representation of the graph.
The incidence list representation is a list of lists. Each item of the outer list belongs to a single vertex of the graph. The inner list contains the IDs of the incident edges of the given vertex.
Parameters  
mode  if "out", returns the successors of the vertex. If "in", returns the predecessors of the vertex. If "all", both the predecessors and the successors will be returned. Ignored for undirected graphs. 
Export vertices with attributes to pandas.DataFrame
If you want to use vertex names as index, you can do:
>>> from string import ascii_letters >>> graph = Graph.GRG(25, 0.4) >>> graph.vs["name"] = ascii_letters[:graph.vcount()] >>> df = graph.get_vertex_dataframe() >>> df.set_index('name', inplace=True)
Returns  
a pandas.DataFrame representing vertices and their attributes. The index uses vertex IDs, from 0 to N  1 where N is the number of vertices. 
igraph._igraph.GraphBase.gomory_hu_tree
Calculates the GomoryHu tree of an undirected graph with optional edge capacities.
The GomoryHu tree is a concise representation of the value of all the maximum flows (or minimum cuts) in a graph. The vertices of the tree correspond exactly to the vertices of the original graph in the same order. Edges of the GomoryHu tree are annotated by flow values. The value of the maximum flow (or minimum cut) between an arbitrary (u,v) vertex pair in the original graph is then given by the minimum flow value (i.e. edge annotation) along the shortest path between u and v in the GomoryHu tree.
Parameters  
capacity  the edge capacities (weights). If None, all edges have equal weight. May also be an attribute name. 
flow  the name of the edge attribute in the returned graph in which the flow values will be stored. 
Returns  
the GomoryHu tree as a Graph object. 
Creates the intersection of two (or more) graphs.
Parameters  
other  graph or list of graphs to be intersected with the current one. 
byname  whether to use vertex names instead of ids. See igraph.intersection for details. 
Returns  
the intersection graph 
Returns whether the graph is named.
A graph is named if and only if it has a "name" vertex attribute.
Returns whether the graph is weighted.
A graph is weighted if and only if it has a "weight" edge attribute.
Returns some kcores of the graph.
The method accepts an arbitrary number of arguments representing the desired indices of the kcores to be returned. The arguments can also be lists or tuples. The result is a single Graph
object if an only integer argument was given, otherwise the result is a list of Graph
objects representing the desired kcores in the order the arguments were specified. If no argument is given, returns all kcores in increasing order of k.
Returns the layout of the graph according to a layout algorithm.
Parameters and keyword arguments not specified here are passed to the layout algorithm directly. See the documentation of the layout algorithms for the explanation of these parameters.
Registered layout names understood by this method are:
 auto, automatic: automatic layout (see
layout_auto
)  bipartite: bipartite layout (see
layout_bipartite
)  circle, circular: circular layout (see
layout_circle
)  dh, davidson_harel: DavidsonHarel layout (see
layout_davidson_harel
)  drl: DrL layout for large graphs (see
layout_drl
)  drl_3d: 3D DrL layout for large graphs (see
layout_drl
)  fr, fruchterman_reingold: FruchtermanReingold layout (see
layout_fruchterman_reingold
).  fr_3d, fr3d, fruchterman_reingold_3d: 3D Fruchterman Reingold layout (see
layout_fruchterman_reingold
).  grid: regular grid layout in 2D (see
layout_grid
)  grid_3d: regular grid layout in 3D (see
layout_grid_3d
)  graphopt: the graphopt algorithm (see
layout_graphopt
)  kk, kamada_kawai: KamadaKawai layout (see
layout_kamada_kawai
)  kk_3d, kk3d, kamada_kawai_3d: 3D KamadaKawai layout (see
layout_kamada_kawai
)  lgl, large, large_graph: Large Graph Layout (see
layout_lgl
)  mds: multidimensional scaling layout (see
layout_mds
)  random: random layout (see
layout_random
)  random_3d: random 3D layout (see
layout_random
)  rt, tree, reingold_tilford: ReingoldTilford tree layout (see
layout_reingold_tilford
)  rt_circular, reingold_tilford_circular: circular ReingoldTilford tree layout (see
layout_reingold_tilford_circular
)  sphere, spherical, circle_3d, circular_3d: spherical layout (see
layout_circle
)  star: star layout (see
layout_star
)  sugiyama: Sugiyama layout (see
layout_sugiyama
)
Parameters  
layout  the layout to use. This can be one of the registered layout names or a callable which returns either a Layout object or a list of lists containing the coordinates. If None, uses the value of the plotting.layout configuration key. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
a Layout object. 
Chooses and runs a suitable layout function based on simple topological properties of the graph.
This function tries to choose an appropriate layout function for the graph using the following rules:
 If the graph has an attribute called layout, it will be used. It may either be a
Layout
instance, a list of coordinate pairs, the name of a layout function, or a callable function which generates the layout when called with the graph as a parameter.  Otherwise, if the graph has vertex attributes called x and y, these will be used as coordinates in the layout. When a 3D layout is requested (by setting dim to 3), a vertex attribute named z will also be needed.
 Otherwise, if the graph is connected and has at most 100 vertices, the KamadaKawai layout will be used (see
layout_kamada_kawai()
).  Otherwise, if the graph has at most 1000 vertices, the FruchtermanReingold layout will be used (see
layout_fruchterman_reingold()
).  If everything else above failed, the DrL layout algorithm will be used (see
layout_drl()
).
All the arguments of this function except dim are passed on to the chosen layout function (in case we have to call some layout function).
Parameters  
*args  Undocumented 
**kwds  Undocumented 
dim  specifies whether we would like to obtain a 2D or a 3D layout. 
Returns  
a Layout object. 
Places the vertices using a layered Sugiyama layout.
This is a layered layout that is most suitable for directed acyclic graphs, although it works on undirected or cyclic graphs as well.
Each vertex is assigned to a layer and each layer is placed on a horizontal line. Vertices within the same layer are then permuted using the barycenter heuristic that tries to minimize edge crossings.
Dummy vertices will be added on edges that span more than one layer. The returned layout therefore contains more rows than the number of nodes in the original graph; the extra rows correspond to the dummy vertices.
Parameters  
layers  a vector specifying a nonnegative integer layer index for each vertex, or the name of a numeric vertex attribute that contains the layer indices. If None, a layering will be determined automatically. For undirected graphs, a spanning tree will be extracted and vertices will be assigned to layers using a breadth first search from the node with the largest degree. For directed graphs, cycles are broken by reversing the direction of edges in an approximate feedback arc set using the heuristic of Eades, Lin and Smyth, and then using longest path layering to place the vertices in layers. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
hgap  minimum horizontal gap between vertices in the same layer. 
vgap  vertical gap between layers. The layer index will be multiplied by vgap to obtain the Y coordinate. 
maxiter  maximum number of iterations to take in the crossing reduction step. Increase this if you feel that you are getting too many edge crossings. 
return  specifies that the extended graph with the added dummy vertices should also be returned. When this is True, the result will be a tuple containing the layout and the extended graph. The first V nodes of the extended graph will correspond to the nodes of the original graph, the remaining ones are dummy nodes. Plotting the extended graph with the returned layout and hidden dummy nodes will produce a layout that is similar to the original graph, but with the added edge bends. The extended graph also contains an edge attribute called _original_eid which specifies the ID of the edge in the original graph from which the edge of the extended graph was created. 
Returns  
the calculated layout, which may (and usually will) have more rows than the number of vertices; the remaining rows correspond to the dummy nodes introduced in the layering step. When return_extended_graph is True, it will also contain the extended graph.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
K Sugiyama, S Tagawa, M Toda: Methods for visual understanding of hierarchical system structures. IEEE Systems, Man and Cybernetics 11(2):109125, 1981.  
P Eades, X Lin and WF Smyth: A fast effective heuristic for the feedback arc set problem. Information Processing Letters 47:319323, 1993. 
igraph._igraph.GraphBase.maxflow
Returns a maximum flow between the given source and target vertices in a graph.
A maximum flow from source to target is an assignment of nonnegative real numbers to the edges of the graph, satisfying two properties:
 For each edge, the flow (i.e. the assigned number) is not more than the capacity of the edge (see the capacity argument)
 For every vertex except the source and the target, the incoming flow is the same as the outgoing flow.
The value of the flow is the incoming flow of the target or the outgoing flow of the source (which are equal). The maximum flow is the maximum possible such value.
Parameters  
source  Undocumented 
target  Undocumented 
capacity  the edge capacities (weights). If None, all edges have equal weight. May also be an attribute name. 
Returns  
a Flow object describing the maximum flow 
Finds a maximum matching in a bipartite graph.
A maximum matching is a set of edges such that each vertex is incident on at most one matched edge and the number (or weight) of such edges in the set is as large as possible.
Parameters  
types  vertex types in a list or the name of a vertex attribute holding vertex types. Types should be denoted by zeros and ones (or False and True) for the two sides of the bipartite graph. If omitted, it defaults to type, which is the default vertex type attribute for bipartite graphs. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
eps  a small real number used in equality tests in the weighted bipartite matching algorithm. Two real numbers are considered equal in the algorithm if their difference is smaller than this value. This is required to avoid the accumulation of numerical errors. If you pass None here, igraph will try to determine an appropriate value automatically. 
Returns  
an instance of Matching . 
igraph._igraph.GraphBase.mincut
Calculates the minimum cut between the given source and target vertices or within the whole graph.
The minimum cut is the minimum set of edges that needs to be removed to separate the source and the target (if they are given) or to disconnect the graph (if neither the source nor the target are given). The minimum is calculated using the weights (capacities) of the edges, so the cut with the minimum total capacity is calculated.
For undirected graphs and no source and target, the method uses the StoerWagner algorithm. For a given source and target, the method uses the pushrelabel algorithm; see the references below.
Parameters  
source  the source vertex ID. If None, the target must also be None and the calculation will be done for the entire graph (i.e. all possible vertex pairs). 
target  the target vertex ID. If None, the source must also be None and the calculation will be done for the entire graph (i.e. all possible vertex pairs). 
capacity  the edge capacities (weights). If None, all edges have equal weight. May also be an attribute name. 
Returns  
a Cut object describing the minimum cut 
igraph._igraph.GraphBase.modularity
Calculates the modularity score of the graph with respect to a given clustering.
The modularity of a graph w.r.t. some division measures how good the division is, or how separated are the different vertex types from each other. It's defined as Q = 1 ⁄ (2m)*sum(Aij − ki*kj ⁄ (2m)delta(ci, cj), i, j). m is the number of edges, Aij is the element of the A adjacency matrix in row i and column j, ki is the degree of node i, kj is the degree of node j, and Ci and cj are the types of the two vertices (i and j). delta(x, y) is one iff x = y, 0 otherwise.
If edge weights are given, the definition of modularity is modified as follows: Aij becomes the weight of the corresponding edge, ki is the total weight of edges adjacent to vertex i, kj is the total weight of edges adjacent to vertex j and m is the total edge weight in the graph.
Parameters  
membership  a membership list or a VertexClustering object 
weights  optional edge weights or None if all edges are weighed equally. Attribute names are also allowed. 
Returns  
the modularity score  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
MEJ Newman and M Girvan: Finding and evaluating community structure in networks. Phys Rev E 69 026113, 2004. 
Calculates the PageRank values of a graph.
Parameters  
vertices  the indices of the vertices being queried. None means all of the vertices. 
directed  whether to consider directed paths. 
damping  the damping factor. 1 − damping is the PageRank value for nodes with no incoming links. It is also the probability of resetting the random walk to a uniform distribution in each step. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
arpack  an ARPACKOptions object used to finetune the ARPACK eigenvector calculation. If omitted, the modulelevel variable called arpack_options is used. This argument is ignored if not the ARPACK implementation is used, see the implementation argument. 
implementation  which implementation to use to solve the PageRank eigenproblem. Possible values are:

niter  The number of iterations to use in the power method implementation. It is ignored in the other implementations 
eps  The power method implementation will consider the calculation as complete if the difference of PageRank values between iterations change less than this value for every node. It is ignored by the other implementations. 
Returns  
a list with the Google PageRank values of the specified vertices. 
Returns the path length histogram of the graph
Parameters  
directed  whether to consider directed paths. Ignored for undirected graphs. 
Returns  
a Histogram object. The object will also have an unconnected attribute that stores the number of unconnected vertex pairs (where the second vertex can not be reached from the first one). The latter one will be of type long (and not a simple integer), since this can be very large. 
Calculates a minimum spanning tree for a graph.
Parameters  
weights  a vector containing weights for every edge in the graph. None means that the graph is unweighted. 
return  whether to return the minimum spanning tree (when return_tree is True) or to return the IDs of the edges in the minimum spanning tree instead (when return_tree is False). The default is True for historical reasons as this argument was introduced in igraph 0.6. 
Returns  
the spanning tree as a Graph object if return_tree is True or the IDs of the edges that constitute the spanning tree if return_tree is False.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Prim, R.C.: Shortest connection networks and some generalizations. Bell System Technical Journal 36:13891401, 1957. 
igraph._igraph.GraphBase.st_mincut
Calculates the minimum cut between the source and target vertices in a graph.
Parameters  
source  the source vertex ID 
target  the target vertex ID 
capacity  the capacity of the edges. It must be a list or a valid attribute name or None. In the latter case, every edge will have the same capacity. 
Returns  
the value of the minimum cut, the IDs of vertices in the first and second partition, and the IDs of edges in the cut, packed in a 4tuple 
Returns the summary of the graph.
The output of this method is similar to the output of the __str__ method. If verbosity is zero, only the header line is returned (see __str__ for more details), otherwise the header line and the edge list is printed.
Behind the scenes, this method constructs a GraphSummary
object and invokes its __str__ method.
Parameters  
verbosity  if zero, only the header line is returned (see __str__ for more details), otherwise the header line and the full edge list is printed. 
width  the number of characters to use in one line. If None, no limit will be enforced on the line lengths. 
*args  Undocumented 
**kwds  Undocumented 
Returns  
the summary of the graph. 
Converts the graph to graphtool
Data types: graphtool only accepts specific data types. See the following web page for a list:
https://graphtool.skewed.de/static/doc/quickstart.html
Note: because of the restricted data types in graphtool, vertex and edge attributes require to be typeconsistent across all vertices or edges. If you set the property for only some vertices/edges, the other will be tagged as None in pythonigraph, so they can only be converted to graphtool with the type 'object' and any other conversion will fail.
Parameters  
graph  dictionary of graph attributes to transfer. Keys are attributes from the graph, values are data types (see below). None means no graph attributes are transferred. 
vertex  dictionary of vertex attributes to transfer. Keys are attributes from the vertices, values are data types (see below). None means no vertex attributes are transferred. 
edge  dictionary of edge attributes to transfer. Keys are attributes from the edges, values are data types (see below). None means no vertex attributes are transferred. 
Converts the graph to networkx format.
Parameters  
create  specifies which NetworkX graph class to use when constructing the graph. None means to let igraph infer the most appropriate class based on whether the graph is directed and whether it has multiedges. 
Calculates the average of the vertex transitivities of the graph.
In the unweighted case, the transitivity measures the probability that two neighbors of a vertex are connected. In case of the average local transitivity, this probability is calculated for each vertex and then the average is taken. Vertices with less than two neighbors require special treatment, they will either be left out from the calculation or they will be considered as having zero transitivity, depending on the mode parameter. The calculation is slightly more involved for weighted graphs; in this case, weights are taken into account according to the formula of Barrat et al (see the references).
Note that this measure is different from the global transitivity measure (see transitivity_undirected()
) as it simply takes the average local transitivity across the whole network.
Parameters  
mode  defines how to treat vertices with degree less than two. If TRANSITIVITY_ZERO or "zero", these vertices will have zero transitivity. If TRANSITIVITY_NAN or "nan", these vertices will be excluded from the average. 
weights  edge weights to be used. Can be a sequence or iterable or even an edge attribute name. 
See Also  
transitivity_undirected() , transitivity_local_undirected()  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Watts DJ and Strogatz S: Collective dynamics of smallworld networks. Nature 393(6884):440442, 1998.  
Barrat A, Barthelemy M, PastorSatorras R and Vespignani A: The architecture of complex weighted networks. PNAS 101, 3747 (2004). http://arxiv.org/abs/condmat/0311416. 
igraph._igraph.GraphBase.triad_census
Calculates the triad census of the graph.
Returns  
a TriadCensus object.  
Unknown Field: newfield  
ref  Reference 
Unknown Field: ref  
Davis, J.A. and Leinhardt, S. (1972). The Structure of Positive Interpersonal Relations in Small Groups. In: J. Berger (Ed.), Sociological Theories in Progress, Volume 2, 218251. Boston: Houghton Mifflin. 
Creates the union of two (or more) graphs.
Parameters  
other  graph or list of graphs to be united with the current one. 
byname  whether to use vertex names instead of ids. See igraph.union for details. 
Returns  
the union graph 
Unified writing function for graphs.
This method tries to identify the format of the graph given in the first parameter (based on extension) and calls the corresponding writer method.
The remaining arguments are passed to the writer method without any changes.
Parameters  
f  the file containing the graph to be saved 
format  the format of the file (if one wants to override the format determined from the filename extension, or the filename itself is a stream). None means autodetection. Possible values are:

*args  Undocumented 
**kwds  Undocumented 
Raises  
IOError  if the file format can't be identified and none was given. 
Writes the adjacency matrix of the graph to the given file
All the remaining arguments not mentioned here are passed intact to Graph.get_adjacency
.
Parameters  
f  the name of the file to be written. 
sep  the string that separates the matrix elements in a row 
eol  the string that separates the rows of the matrix. Please note that igraph is able to read back the written adjacency matrix if and only if this is a single newline character 
*args  Undocumented 
**kwds  Undocumented 
igraph._igraph.GraphBase.write_dimacs
Writes the graph in DIMACS format to the given file.
Parameters  
f  the name of the file to be written or a Python file handle. 
source  the source vertex ID. If None, igraph will try to infer it from the source graph attribute. 
target  the target vertex ID. If None, igraph will try to infer it from the target graph attribute. 
capacity  the capacities of the edges in a list or the name of an edge attribute that holds the capacities. If there is no such edge attribute, every edge will have a capacity of 1. 
Writes the graph to a zipped GraphML file.
The library uses the gzip compression algorithm, so the resulting file can be unzipped with regular gzip uncompression (like gunzip or zcat from Unix command line) or the Python gzip module.
Uses a temporary file to store intermediate GraphML data, so make sure you have enough free space to store the unzipped GraphML file as well.
Parameters  
f  the name of the file to be written. 
compresslevel  the level of compression. 1 is fastest and produces the least compression, and 9 is slowest and produces the most compression. 
Saves the graph in Python pickled format
Parameters  
fname  the name of the file or a stream to save to. If None, saves the graph to a string and returns the string. 
version  pickle protocol version to be used. If 1, uses the highest protocol available 
Returns  
None if the graph was saved successfully to the given file, or a string if fname was None. 
Saves the graph in Python pickled format, compressed with gzip.
Saving in this format is a bit slower than saving in a Python pickle without compression, but the final file takes up much less space on the hard drive.
Parameters  
fname  the name of the file or a stream to save to. 
version  pickle protocol version to be used. If 1, uses the highest protocol available 
Returns  
None if the graph was saved successfully to the given file. 
Saves the graph as an SVG (Scalable Vector Graphics) file
The file will be Inkscape (http://inkscape.org) compatible. In Inkscape, as nodes are rearranged, the edges autoupdate.
Parameters  
fname  the name of the file or a Python file handle 
layout  the layout of the graph. Can be either an explicitly specified layout (using a list of coordinate pairs) or the name of a layout algorithm (which should refer to a method in the Graph object, but without the layout_ prefix. 
width  the preferred width in pixels (default: 400) 
height  the preferred height in pixels (default: 400) 
labels  the vertex labels. Either it is the name of a vertex attribute to use, or a list explicitly specifying the labels. It can also be None. 
colors  the vertex colors. Either it is the name of a vertex attribute to use, or a list explicitly specifying the colors. A color can be anything acceptable in an SVG file. 
shapes  the vertex shapes. Either it is the name of a vertex attribute to use, or a list explicitly specifying the shapes as integers. Shape 0 means hidden (nothing is drawn), shape 1 is a circle, shape 2 is a rectangle and shape 3 is a rectangle that automatically sizes to the inner text. 
vertex  vertex size in pixels 
edge  the edge colors. Either it is the name of an edge attribute to use, or a list explicitly specifying the colors. A color can be anything acceptable in an SVG file. 
edge  the stroke widths of the edges. Either it is the name of an edge attribute to use, or a list explicitly specifying the stroke widths. The stroke width can be anything acceptable in an SVG file. 
font  font size. If it is a string, it is written into the SVG file asis (so you can specify anything which is valid as the value of the fontsize style). If it is a number, it is interpreted as pixel size and converted to the proper attribute value accordingly. 
*args  Undocumented 
**kwds  Undocumented 
_identify_format(filename)
Tries to identify the format of the graph stored in the file with the given filename. It identifies most file formats based on the extension of the file (and not on syntactic evaluation). The only exception is the adjacency matrix format and the edge list format: the first few lines of the file are evaluated to decide between the two.
Parameters  
filename  the name of the file or a file object whose name attribute is set. 
Returns  
the format of the file as a string.  
Note  
Internal function, should not be called directly. 