Generating graphs for given degree sequence in Python or R

Question

I am trying to learn if in Python or R, there exist within the graph-theory related modules features that would enable one to start from a degree distribution (or expressed as a sequence once we set the number of vertices), and generate (random) graphs that satisfy the prescribed degree sequence.

As an example, we might be given the following distribution: p=(0.179,0.49,0.34) which are the probabilities of degree values 1,2 and 3 respectively. So we can set the number of vertices, n=500, map p to a degree sequence deseq list: filled with 0.179*n times of 1, and so on for the rest.

Any pointers towards previously discussed cases for such problems or library suggestions would be very helpful.

Answer 1

Here's an attempt to answer my own question after having learned how to use igraph in R and Python for generating the desired type of graphs.

In R:

For the purposes of this example, let's suppose the following degree sequence: total nodes n=20, 5,10 and 5 nodes with degrees 1,2, and 3 respectively. We create the degree sequence using c() and rep(). Then we'll use sample_degseq() from igraph to generate a graph corresponding to the above degree sequence. Then we'll draw its degree histogram to sanity check.

First install and call the igraph module in the R console using:

install.packages("igraph")
library(igraph)

Now we can proceed as described:

degreels <- c(rep(1,5),rep(2,10),rep(3,5))
graph <- sample_degseq(degreels, method="simple")
degreehist <- hist(degree(graph))
is.connected(graph)

In Python:

Now let's do the exact same thing with the igraph module in Python:

To install see here.

import igraph as ig
import matplotlib.pyplot as plt

degcounts = [5,10,5]
degreels = []
for i in range(len(degcounts)):
    degreels += degcounts[i]*[i+1]

graph = ig.GraphBase.Degree_Sequence(degreels,method="simple")
plt.hist(graph.degree())
plt.show()

and the obtained histogram:

Answer 2

I don't know how much have you already researched on the topic but there is a pretty wellknown package in R and module in Python called igraph. It might have what you seek for.