Master NetworkX: Install, Build Weighted Graphs, and Find Shortest Paths in Python

NetworkX is a Python library for graph theory and complex network modeling, providing built‑in algorithms for analysis, simulation, and visualization.

1. Installing and Importing NetworkX

Install via pip:

<code>pip install networkx</code>

If using Anaconda, the library is already available and is typically imported as nx :

<code>import networkx as nx</code>

Commonly used functions include creating graphs, adding nodes or edges, and computing shortest paths.

Graph() : create an undirected graph

Graph(A) : create an undirected graph from adjacency matrix A

DiGraph() : create a directed graph

DiGraph(A) : create a directed graph from adjacency matrix A

MultiGraph() : create a multigraph

MultiDiGraph() : create a multidigraph

add_edge() : add a single edge

add_edges_from(List) : add multiple edges from a list

add_node() : add a single node

add_nodes_from(List) : add a collection of nodes

dijkstra_path(G, source, target, weight='weight') : compute the shortest path

dijkstra_path_length(G, source, target, weight='weight') : compute the shortest distance

2. Building a Weighted Undirected Graph

Define a weighted adjacency matrix (zero indicates no direct connection) and convert it to a NetworkX graph:

<code>import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
a = np.array([[0.,9.,2.,4.,7.],
              [9.,0.,3.,4.,0.],
              [2.,3.,0.,8.,4.],
              [4.,4.,8.,0.,6.],
              [7.,0.,4.,6.,0.]])
a1 = pd.DataFrame(a, index=range(1,6), columns=range(1,6))
G = nx.from_numpy_array(a1)
G.edges(data=True)  # show weights
</code>

Draw the graph with edge weights:

<code>pos = nx.shell_layout(G)  # layout
nx.draw_networkx(G, pos, node_size=260)
w = nx.get_edge_attributes(G, 'weight')
nx.draw_networkx_edge_labels(G, pos, font_size=12, edge_labels=w)
plt.savefig('images/net0102.png')
plt.show()
</code>

Five layout options are available: circular_layout , random_layout , shell_layout , spring_layout (Fruchterman‑Reingold), and spectral_layout .

3. Finding Shortest Paths

NetworkX provides several shortest‑path algorithms such as Dijkstra and Floyd. Example using Dijkstra:

<code>nx.shortest_path(G, 5, 2, weight='weight')
# returns [5, 3, 2]

nx.shortest_path_length(G, 5, 2, weight='weight')
# returns 7
</code>

4. Computing a Minimum Spanning Tree

Both Kruskal and Prim algorithms are available via minimum_spanning_tree :

<code>tree_min = nx.minimum_spanning_tree(G, weight='weight')
pos = nx.shell_layout(G)
nx.draw_networkx(tree_min, pos, node_size=260)
w = nx.get_edge_attributes(tree_min, 'weight')
nx.draw_networkx_edge_labels(tree_min, pos, font_size=12, edge_labels=w)
plt.savefig('images/net0103.png')
plt.show()
</code>

Reference

Python数学实验与建模 / 司守奎, 孙玺菁, 科学出版社