Exercise 01

Complex Networks INPE 2025

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

1. read an adjacency matrix from a file
2. calculate the number of nodes and edges
3. promote different graph’s visualizations
4. think about different metrics on the graph

1. Matrix load

Adjacency matrix creation based on numpy methods:

np.random.seed(123)

A = np.random.randint(0, 2, size=(10, 10))
A = np.triu(A, 1)
A = A + A.T

Now the graph can be created, based on matrix A:

G = nx.from_numpy_array(A)

2. Nodes and edges

Counting nodes and edges:

print(f'Nodes: {len(G.nodes)}')
print(f'Edges: {len(G.edges)}')

Nodes: 10
Edges: 17

3. Visualization

Using matplotlib and nx.draw:

plt.figure(figsize=(8, 5), dpi=300)
nx.draw(
    G,
    with_labels=True,
    node_color='lightblue',
    edge_color='grey',
    node_size=1000,
    font_size=10,
)

plt.show()

4. Metrics

4.1 Global metrics

Average shortest path length:

print(nx.average_shortest_path_length(G))

1.7777777777777777

4.2 Node metrics

Betweenness:

betweenness = nx.betweenness_centrality(G)
plt.figure(figsize=(8, 5), dpi=300)
pos = nx.spring_layout(G, seed=42)
nodes = nx.draw_networkx_nodes(
    G,
    pos,
    node_color=list(betweenness.values()),
    node_size=1000
)
edges = nx.draw_networkx_edges(G, pos, alpha=0.4)
labels = nx.draw_networkx_labels(G, pos, font_size=10)
plt.colorbar(nodes, label="Betweenness Centrality")