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degree_centrality¶
- degree_centrality(G, nodes)[source]¶
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 : G : graph
A bipartite network
nodes : list or container
Container with all nodes in one bipartite node set.
Returns : centrality : dictionary
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 conatin all nodes in one bipartite node set, but the dictionary returned contains all nodes from both bipartite node sets.
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 [R156]. The degree centrality for a node \(v\) in the bipartite sets \(U\) with \(n\) nodes and \(V\) with \(m\) nodes is
\[d_{v} = \frac{deg(v)}{m}, \mbox{for} v \in U ,\]\[d_{v} = \frac{deg(v)}{n}, \mbox{for} v \in V ,\]where \(deg(v)\) is the degree of node \(v\).
References
[R156] (1, 2) 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. http://www.steveborgatti.com/papers/bhaffiliations.pdf