Concept of projection

Intermediate Network Analysis in Python

Eric Ma

Data Carpentry instructor and author of nxviz package

Projection

Useful to investigate the relationships between nodes on one partition
- Conditioned on the connections to the nodes in the other partition

Projection

Unipartite representation of bipartite connectivity

ch2-1.006.png

Projection

Unipartite representation of bipartite connectivity

ch2-1.007.png

Projection

Unipartite representation of bipartite connectivity

ch2-1.008.png

Projection

Unipartite representation of bipartite connectivity

ch2-1.009.png

Graphs on Disk

Flat edge lists
CSV files: nodelist + metadata, edgelist + metadata

Reading network data

import networkx as nx
G = nx.read_edgelist('american-revolution.txt')

list(G.edges(data=True))[0:5]

[('Parkman.Elias', 'LondonEnemies', {'weight': 1}),
 ('Parkman.Elias', 'NorthCaucus', {'weight': 1}),
 ('Inglish.Alexander', 'StAndrewsLodge', {'weight': 1}),
 ('NorthCaucus', 'Chadwell.Mr', {'weight': 1}),
 ('NorthCaucus', 'Pearce.IsaacJun', {'weight': 1})]

Text File

Barrett.Samuel LondonEnemies {'weight': 1}
Barrett.Samuel StAndrewsLodge {'weight': 1}
Marshall.Thomas LondonEnemies {'weight': 1}
Eaton.Joseph TeaParty {'weight': 1}
Bass.Henry LondonEnemies {'weight': 1}

Bipartite projection

list(G.nodes())

['product2', 'customer3', 'customer1', 'product3',  
    'customer2', 'product1']

list(G.edges())

[('product2', 'customer1'),
 ('product2', 'customer2'),
 ('customer3', ‘product1')]

Bipartite projection

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

['customer3', 'customer1', 'customer2']

Bipartite projection

G_cust = nx.bipartite.projected_graph(G, cust_nodes)
list(G_cust.nodes())

['customer1', 'customer3', 'customer2']

list(G_cust.edges())

[('customer1', 'customer2')]

Degree centrality

Recall degree centrality definition $$\frac{\text{number of neighbors}}{\text{number of possible neighbors}}$$
Denominator: number of nodes on opposite partition

Bipartite degree centrality

nx.bipartite.degree_centrality(G, cust_nodes)

{'customer1': 0.3333333333333333,
 'customer2': 0.3333333333333333,
 'customer3': 0.3333333333333333,
 'product1': 0.3333333333333333,
 'product2': 0.6666666666666666,
 'product3': 0.0}

Bipartite degree centrality

nx.degree_centrality(G)

{'customer1': 0.2,
 'customer2': 0.2,
 'customer3': 0.2,
 'product1': 0.2,
 'product2': 0.4,
 'product3': 0.0}

Let's practice!

Intermediate Network Analysis in Python