Bipartite graphs

Intermediate Network Analysis in Python

Eric Ma

Data Carpentry instructor and author of nxviz package

Bipartite graphs

A graph that is partitioned into two sets
Nodes are only connected to nodes in other partitions
Contrast: "unipartite"

Bipartite graphs: Example

ch1-2.007.png

Bipartite graphs in NetworkX

import networkx as nx
G = nx.Graph()

numbers = range(3)
G.add_nodes_from(numbers, bipartite='customers')

letters = ['a', 'b']
G.add_nodes_from(letters, bipartite='products')

Bipartite graphs in NetworkX

list(G.nodes(data=True))

[(0, {'bipartite': 'customers'}),
 (1, {'bipartite': 'customers'}),
 (2, {'bipartite': 'customers'}),
 ('b', {'bipartite': 'products'}),
 ('a', {'bipartite': 'products'})]

Degree centrality

Definition: $$\frac{\text{number of neighbors}}{\text{number of possible neighbors}}$$
Number of possible neighbors depends on graph type

Bipartite centrality metrics

Denominator: number of nodes in opposite partition, rather than all other nodes

ch1-2.021.png

Filtering graphs

cust_nodes = [n for n, d in G.nodes(data=True) if  
                  d['bipartite'] == 'customers']

cust_nodes

[(0, {'bipartite': 'customers'}),
 (1, {'bipartite': 'customers'}),
 (2, {'bipartite': 'customers'})]

nx.bipartite.degree_centrality(G, cust_nodes)

{0: 0.5,
 1: 0.5,
 2: 1.0,
 'a': 0.333,
 'b': 1.0}

Let's practice!

Intermediate Network Analysis in Python