Random graphs with two-sided degree bounds

I wanted some random examples of graphs where every vertex has degree between two given parameters, minDegree and maxDegree. Like this one:

15 vertices, degree from 3 to 4
15 vertices, degree from 3 to 4

The approach I took was very simple (and not suitable for construction of very large or very regular graphs). Each edge appears with probability p. If the minimal degree is too small, this probability is multiplied by 1.1. If the maximal degree is too big, the probability is divided by 1.1. Either way, the process repeats until success.

20 vertices, degree from 1 to 5

So far, this blog had too much Matlab/Scilab and not enough Python. I’ll try to restore the balance. Here, numpy generates random matrices and takes care of degree restrictions; networkx lays out the graph.

import numpy as np
import networkx as nx
import matplotlib.pyplot as plt

vertices = 15
minDegree = 3
maxDegree = 4
p = 0.5
success = False

while not success:
    a = (np.random.random((vertices, vertices)) < p).astype(int)
    a = np.maximum(a, np.matrix.transpose(a))
    np.fill_diagonal(a, 0)
    s = a.sum(axis=1)
    success = True
    if min(s) < minDegree:
        success = False
        p = p * 1.1
    if max(s) > maxDegree:
        success = False
        p = p / 1.1
g = nx.Graph(a)

One more time:

25 vertices, degree from 2 to 4

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