Graph generation

• Graph generation
  • From nodes and edges
  • From matrices
  • From file
  • From external libraries
  • From pandas DataFrame(s)
  • From a formula
  • Full graphs
  • Tree and star
  • Lattice
  • Graph Atlas
  • Famous graphs
  • Random graphs
  • Other graphs

Graph generation

The first step of most igraph applications is to generate a graph. This section will explain a number of ways to do that. Read the API documentation for details on each function and class.

The Graph class is the main object used to generate graphs:

>>> from igraph import Graph

To copy a graph, use Graph.copy():

>>> g_new = g.copy()

From nodes and edges

Nodes are always numbered from 0 upwards. To create a generic graph with a specified number of nodes (e.g. 10) and a list of edges between them, you can use the generic constructor:

>>> g = Graph(n=10, edges=[[0, 1], [2, 3]])

If not specified, the graph is undirected. To make a directed graph:

>>> g = Graph(n=10, edges=[[0, 1], [2, 3]], directed=True)

To specify edge weights (or any other vertex/edge attributes), use dictionaries:

>>> g = Graph(
...     n=4, edges=[[0, 1], [2, 3]],
...     edge_attrs={'weight': [0.1, 0.2]},
...     vertex_attrs={'color': ['b', 'g', 'g', 'y']}
... )

Variations on this constructor is Graph.DictList(), which constructs a graph from a list-of-dictionaries representation, and Graph.TupleList(), which constructs a graph from a list-of-tuples representation.

To create a bipartite graph from a list of types and a list of edges, use Graph.Bipartite().

From matrices

To create a graph from an adjecency matrix, use Graph.Adjacency() or, for weighted matrices, Graph.Weighted_Adjacency():

>>> g = Graph.Adjacency([[0, 1, 1], [0, 0, 0], [0, 0, 1]])

This graph is directed and has edges [0, 1], [0, 2] and [2, 2] (a loop).

To create a bipartite graph from an incidence matrix, use Graph.Incidence():

>>> g = Graph.Incidence([[0, 1, 1], [1, 1, 0]])

From file

To load a graph from a preexisting file in any of the supported formats, use Graph.Load(). For instance:

>>> g = Graph.Load('myfile.gml', format='gml')

If you don’t specify a format, igraph will try to figure it out or, if that fails, it will complain.

From external libraries

igraph can read from and write to networkx and graph-tool graph formats:

>>> g = Graph.from_networkx(nwx)

and

>>> g = Graph.from_graph_tool(gt)

From pandas DataFrame(s)

A common practice is to store edges in a pandas.DataFrame, where the two first columns are the source and target vertex ids, and any additional column indicates edge attributes. You can generate a graph via Graph.DataFrame():

>>> g = Graph.DataFrame(edges, directed=False)

It is possible to set vertex attributes at the same time via a separate DataFrame. The first column is assumed to contain all vertex ids (including any vertices without edges) and any additional columns are vertex attributes:

>>> g = Graph.DataFrame(edges, directed=False, vertices=vertices)

From a formula

To create a graph from a string formula, use Graph.Formula(), e.g.:

>>> g = Graph.Formula('D-A:B:F:G, A-C-F-A, B-E-G-B, A-B, F-G, H-F:G, H-I-J')

Note

This particular formula also assigns the ‘name’ attribute to vertices.

Full graphs

To create a full graph, use Graph.Full():

>>> g = Graph.Full(n=3)

where n is the number of nodes. You can specify directedness and whether self loops are allowed:

>>> g = Graph.Full(n=3, directed=True, loops=True)

A similar method, Graph.Full_Bipartite(), generates a full bipartite graph. Finally, the metho Graph.Full_Citation() created the full citation graph, in which each vertex i has a directed edge to all vertices strictly smaller than i.

Tree and star

Graph.Tree() can be used to generate regular trees, in which almost each vertex has the same number of children:

>>> g = Graph.Tree(n=7, n_children=2)

creates a tree with seven vertices - of which four are leaves. The root (0) has two children (1 and 2), each of which has two children (the four leaves). Regular trees can be directed or undirected (default).

The method Graph.Star() creates a star graph, which is a subtype of a tree.

Lattice

Graph.Lattice() creates a regular square lattice of the chosen size. For instance:

>>> g = Graph.Lattice(dim=[3, 3], circular=False)

creates a 3x3 grid in two dimensions (9 vertices total). circular is used to connect each edge of the lattice back onto the other side, a process also known as “periodic boundary condition” that is sometimes helpful to smoothen out edge effects.

The one dimensional case (path graph or cycle graph) is important enough to deserve its own constructor Graph.Ring(), which can be circular or not:

>>> g = Graph.Ring(n=4, circular=False)

Graph Atlas

The book ‘An Atlas of Graphs’ by Roland C. Read and Robin J. Wilson contains all undirected graphs with up to seven vertices, numbered from 0 up to 1252. You can create any graph from this list by index with Graph.Atlas(), e.g.:

>>> g = Graph.Atlas(44)

The graphs are listed:

• in increasing order of number of nodes;

• for a fixed number of nodes, in increasing order of the number of edges;

• for fixed numbers of nodes and edges, in increasing order of the degree sequence, for example 111223 < 112222;

• for fixed degree sequence, in increasing number of automorphisms.

Famous graphs

A curated list of famous graphs, which are often used in the literature for benchmarking and other purposes, is available on the igraph C core manual. You can generate any graph in that list by name, e.g.:

>>> g = Graph.Famous('Zachary')

will teach you some about martial arts.

Random graphs

Stochastic graphs can be created according to several different models or games:

• Barabasi-Albert model: Graph.Barabasi()

• Erdos-Renyi: Graph.Erdos_Renyi()

• Watts-Strogatz Graph.Watts_Strogatz()

• stochastic block model Graph.SBM()

• random tree Graph.Tree_Game()

• forest fire game Graph.Forest_Fire()

• random geometric graph Graph.GRG()

• growing Graph.Growing_Random()

• establishment game Graph.Establishment()

• preference, the non-growing variant of establishment Graph.Preference()

• asymmetric preference Graph.Asymmetric_Prefernce()

• recent degree Graph.Recent_Degree()

• k-regular (each node has degree K) Graph.K_Regular()

• non-growing graph with edge probabilities proportional to node fitnesses Graph.Static_Fitness()

• non-growing graph with prescribed power-law degree distribution(s) Graph.Static_Power_Law()

• random graph with a given degree sequence Graph.Degree_Sequence()

• bipartite Graph.Random_Bipartite()

Other graphs

Finally, there are some ways of generating graphs that are not covered by the previous sections:

• Kautz graphs Graph.Kautz()

• De Bruijn graphs Graph.De_Bruijn()

• Lederberg-Coxeter-Frucht graphs Graph.LCF()

• graphs with a specified isomorphism class Graph.Isoclass()

• graphs with a specified degree sequence Graph.Realize_Degree_Sequence()