Use this if you are using igraph from R
It is often useful to create a graph with given vertex degrees. This function creates such a graph in a deterministic manner.
realize_degseq( out.deg, in.deg = NULL, allowed.edge.types = c("simple", "loops", "multi", "all"), method = c("smallest", "largest", "index") )
out.deg 
Numeric vector, the sequence of degrees (for undirected
graphs) or outdegrees (for directed graphs). For undirected graphs its sum
should be even. For directed graphs its sum should be the same as the sum of

in.deg 
For directed graph, the indegree sequence. By default this is

allowed.edge.types 
Character, specifies the types of allowed edges. “simple” allows simple graphs only (no loops, no multiple edges). “multiple” allows multiple edges but disallows loop. “loops” allows loop edges but disallows multiple edges (currently unimplemented). “all” allows all types of edges. The default is “simple”. 
method 
Character, the method for generating the graph; see above. 
Simple undirected graphs are constructed using the HavelHakimi algorithm (undirected case), or the analogous KleitmanWang algorithm (directed case). These algorithms work by choosing an arbitrary vertex and connecting all its stubs to other vertices. This step is repeated until all degrees have been connected up.
The ‘method’ argument controls in which order the vertices are selected during the course of the algorithm.
The “smallest” method selects the vertex with the smallest remaining degree. The result is usually a graph with high negative degree assortativity. In the undirected case, this method is guaranteed to generate a connected graph, regardless of whether multiedges are allowed, provided that a connected realization exists. In the directed case it tends to generate weakly connected graphs, but this is not guaranteed. This is the default method.
The “largest” method selects the vertex with the largest remaining degree. The result is usually a graph with high positive degree assortativity, and is often disconnected.
The “index” method selects the vertices in order of their index.
The new graph object.
sample_degseq
for a randomized variant that samples
from graphs with the given degree sequence.
g < realize_degseq(rep(2,100)) degree(g) is_simple(g) ## Exponential degree distribution, with high positive assortativity. ## Loop and multiple edges are explicitly allowed. ## Note that we correct the degree sequence if its sum is odd. degs < sample(1:100, 100, replace=TRUE, prob=exp(0.5*(1:100))) if (sum(degs) %% 2 != 0) { degs[1] < degs[1] + 1 } g4 < realize_degseq(degs, method="largest", allowed.edge.types="all") all(degree(g4) == degs) ## Powerlaw degree distribution, no loops allowed but multiple edges ## are okay. ## Note that we correct the degree sequence if its sum is odd. degs < sample(1:100, 100, replace=TRUE, prob=(1:100)^2) if (sum(degs) %% 2 != 0) { degs[1] < degs[1] + 1 } g5 < realize_degseq(degs, allowed.edge.types="multi") all(degree(g5) == degs)