Freeman’s network centrality

Freeman’s centrality tells us how heterogenous is degree centrality ammong vertices of network. For start network, we will get a value 1.

\(FC(g)=\frac{\sum_{x \in g}{N_{max}-|N(x)|}}{(|g|-1)*(|g|-2)}\)

Where \(g\) is given graph, \(N(x)\) returns set of neighbours of vertex \(x\), \(|g|\) is number of vertices in graph \(g\) and \(N_{max}\) is maximal degree that can be observed in network.

For further informations please refer to [Freeman].

import ml.sparkling.graph.operators.OperatorsDSL._
import org.apache.spark.SparkContext
import org.apache.spark.graphx.Graph

implicit ctx:SparkContext=???
// initialize your SparkContext as implicit value
val graph =???
// load your graph (for example using Graph loading API)

val freemanCentrality: Double= graph.freemanCentrality()
// Freeman centrality value for graph

References:

[Freeman]

Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239., PDF