4.1 Inhomogeneous Erdös-Rényi Random Networks

mode = "svg"

import matplotlib

font = {'family' : 'Dejavu Sans',
        'weight' : 'normal',
        'size'   : 20}

matplotlib.rc('font', **font)

import matplotlib
from matplotlib import pyplot as plt

import os
import numpy as np
from graphbook_code import heatmap
from graspologic.simulations import sample_edges

def generate_unit_circle(radius):
    diameter = 2*radius + 1
    rx = ry = diameter/2
    x, y = np.indices((diameter, diameter))

    circle_dist = np.hypot(rx - x, ry - y)
    diff_from_radius = np.abs(circle_dist - radius)
    less_than_half = diff_from_radius < 0.5

    return less_than_half.astype(int)

def add_smile():
    canvas = np.zeros((51, 51))
    canvas[2:45, 2:45] = generate_unit_circle(21)
    mask = np.zeros((51, 51), dtype=bool)
    mask[np.triu_indices_from(mask)] = True
    upper_left = np.rot90(mask)
    canvas[upper_left] = 0
    return canvas
    
def smile_probability(upper_p, lower_p):
    smiley = add_smile()
    P = generate_unit_circle(25)
    P[5:16, 25:36] = generate_unit_circle(5)
    P[smiley != 0] = smiley[smiley != 0]
    
    mask = np.zeros((51, 51), dtype=bool)
    mask[np.triu_indices_from(mask)] = True
    P[~mask] = 0
    # symmetrize the probability matrix
    P = (P + P.T - np.diag(np.diag(P))).astype(float)
    P[P == 1] = lower_p
    P[P == 0] = upper_p
    return P

fig, axs = plt.subplots(1, 2, figsize=(12, 5))
P = smile_probability(.95, 0.05)
heatmap(P, vmin=0, vmax=1, title="(A) Probability matrix $P$",
        legend_title="Edge probability", xtitle="Node", ytitle="Node",
        xticks=[0.5, 24.5, 49.5], xticklabels=[1,25,50],
        yticks=[0.5, 24.5, 49.5], yticklabels=[1,25,50],
        ax=axs[0])

A = sample_edges(P, directed=False, loops=False)
heatmap(A.astype(int), vmin=0, vmax=1, title="(B) $IER_n(P)$ sample",
        legend_title="Edge?", xtitle="Node", ytitle="Node",
        xticks=[0.5, 24.5, 49.5], xticklabels=[1,25,50],
        yticks=[0.5, 24.5, 49.5], yticklabels=[1,25,50],
        ax=axs[1])

fig.tight_layout()

os.makedirs("Figures", exist_ok=True)
fname = "ier"
if mode != "png":
    os.makedirs(f"Figures/{mode:s}", exist_ok=True)
    fig.savefig(f"Figures/{mode:s}/{fname:s}.{mode:s}")

os.makedirs("Figures/png", exist_ok=True)
fig.savefig(f"Figures/png/{fname:s}.png")

import numpy as np
from math import comb

node_count = np.arange(2, 51)
log_unique_network_count = np.array([comb(n, 2) for n in node_count])*np.log10(2)

# plotting code
fig, ax = plt.subplots()
ax.plot(node_count, log_unique_network_count, color="black")
ax.set_xlabel("Number of Nodes")
ax.set_ylabel("Number of Networks\n (log scale)");
ax.set_xticks([10, 20, 30, 40, 50])
ax.set_yticks([0, 100, 200, 300, 400])
ax.set_xlim((0, 50))
ax.set_ylim((0, 400))
fig.tight_layout()

fname = "nnets"
if mode != "png":
    fig.savefig(f"Figures/{mode:s}/{fname:s}.{mode:s}")

fig.savefig(f"Figures/png/{fname:s}.png")