degree_centrality

degree_centrality(G, nodes)

Compute the degree centrality for nodes in a bipartite network.

The degree centrality for a node v is the fraction of nodes connected to it.

Parameters:

Ggraph

A bipartite network

nodeslist or container

Container with all nodes in one bipartite node set.

Returns:

centralitydictionary

Dictionary keyed by node with bipartite degree centrality as the value.

See also

betweenness_centrality

closeness_centrality

sets()

is_bipartite()

Notes

The nodes input parameter must contain all nodes in one bipartite node set, but the dictionary returned contains all nodes from both bipartite node sets. See bipartite documentation for further details on how bipartite graphs are handled in NetworkX.

For unipartite networks, the degree centrality values are normalized by dividing by the maximum possible degree (which is n-1 where n is the number of nodes in G).

In the bipartite case, the maximum possible degree of a node in a bipartite node set is the number of nodes in the opposite node set [1]. The degree centrality for a node v in the bipartite sets U with n nodes and V with m nodes is

\[ \begin{align}\begin{aligned}d_{v} = \frac{deg(v)}{m}, \mbox{for} v \in U ,\\d_{v} = \frac{deg(v)}{n}, \mbox{for} v \in V ,\end{aligned}\end{align} \]

where deg(v) is the degree of node v.

References

[1]

Borgatti, S.P. and Halgin, D. In press. “Analyzing Affiliation Networks”. In Carrington, P. and Scott, J. (eds) The Sage Handbook of Social Network Analysis. Sage Publications. https://dx.doi.org/10.4135/9781446294413.n28

Examples

>>> G = nx.wheel_graph(5)
>>> top_nodes = {0, 1, 2}
>>> nx.bipartite.degree_centrality(G, nodes=top_nodes)
{0: 2.0, 1: 1.5, 2: 1.5, 3: 1.0, 4: 1.0}