neighborhoodConnectivity.rst

Neighborhood Connectivity

Neighborhood connectivity is a measure based on degree centrality. Connectivity of a vertex is its degree. Neighborhood connectivity is average connectivity of neighbours of given vertex.

NC(x)=\frac{\sum_{k \in N(x)}{|N(k)|}}{|N(x)|}

Where N(x) is set of neighbours of vertex x

For further informations please refer to [Maslov].

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 centralityGraph: Graph[Double, _] = graph.neighborhoodConnectivity()
// Graph where each vertex is associated with its neighborhood connectivity

You can also compute neighborhood connectivity for graph treated as undirected one:

import ml.sparkling.graph.operators.OperatorsDSL._
import org.apache.spark.SparkContext
import ml.sparkling.graph.api.operators.measures.VertexMeasureConfiguration
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 centralityGraph: Graph[Double, _] = graph.neighborhoodConnectivity(VertexMeasureConfiguration(treatAsUndirected=true))
// Graph where each vertex is associated with its neighborhood connectivity computed for undirected graph

References:

[Maslov]

Maslov S, Sneppen K . Specificity and stability in topology of protein networks. Science 2002;296:910-913. HTML