Draw graphon Stochastic Block Models

draw_graphon.py

import matplotlibt.pyplot as plt
import numpy as np

plt.figure(figsize=(5,4))
X, Y = np.meshgrid(np.linspace(0,1), np.linspace(0,1))
plt.pcolormesh(X,Y,graphon_val(X,Y,p,n))
plt.colorbar()

graphon_from_sbm.py

import numpy as np
# Define vectorized function which returns the value of the graphon
# at point (x,y) given the stochastic block model of probability matrix
# p and size vector n
def graphon_val(x, y, p, n):
    ns = np.sum(n)
    ncs = np.cumsum(n)
    nx = x * ns
    ny = y * ns
    ix = 0
    iy = 0
    while nx > ncs[ix]:
        ix += 1
    while ny > ncs[iy]:
        iy += 1
    return p[ix, iy]
graphon_val = np.vectorize(graphon_val, excluded=(2,3))

Example with

p = np.array([[0.12, 0.10, 0.10, 0.05, 0.05, 0.00],
              [0.10, 0.12, 0.10, 0.00, 0.05, 0.05],
              [0.10, 0.10, 0.12, 0.05, 0.00, 0.05],
              [0.05, 0.00, 0.05, 0.60, 0.00, 0.00],
              [0.05, 0.05, 0.00, 0.00, 0.60, 0.00],
              [0.00, 0.05, 0.05, 0.00, 0.00, 0.60]])
n = [50, 50, 50, 100, 200, 200]