51. Some Interesting Graphs

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

51.1. ER

https://networkx.org/documentation/stable/auto_examples/graph/plot_erdos_renyi.html

n = 100  # 10 nodes
m = 200  # 20 edges
seed = 42  # seed random number generators for reproducibility

# Use seed for reproducibility
G = nx.gnm_random_graph(n, m, seed=seed)

er_degrees = []
for v in nx.nodes(G):
    er_degrees.append(nx.degree(G, v))


pos = nx.spring_layout(G, seed=seed)  # Seed for reproducible layout
nx.draw(G, pos=pos)
plt.show()

fig, ax = plt.subplots()

ax.hist(er_degrees)

(array([ 1.,  6., 18., 18., 19., 19.,  8.,  5.,  4.,  2.]),
 array([0. , 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9. ]),
 <BarContainer object of 10 artists>)

52. PA

https://networkx.org/documentation/stable/reference/algorithms/generated/networkx.algorithms.link_prediction.preferential_attachment.html?highlight=preferred

n = 100  # 10 nodes
m = 15  # 20 edges
seed = 42  # seed random number generators for reproducibility

# Use seed for reproducibility
G_pa = nx.generators.random_graphs.barabasi_albert_graph(n, m, seed=seed)

# some properties
pa_degrees = []
for v in nx.nodes(G_pa):
    pa_degrees.append(nx.degree(G_pa, v))


pos = nx.spring_layout(G_pa, seed=seed)  # Seed for reproducible layout
nx.draw(G_pa, pos=pos)
plt.show()

fig, ax = plt.subplots()

ax.hist(pa_degrees)

(array([35., 22., 13.,  8.,  3.,  9.,  2.,  2.,  3.,  3.]),
 array([14. , 18.6, 23.2, 27.8, 32.4, 37. , 41.6, 46.2, 50.8, 55.4, 60. ]),
 <BarContainer object of 10 artists>)

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