localClustering.rst

Local Clustering Coefficient

Local Clustering Coefficient for vertex tells us howe close its neighbors are. It's number of existing connections in neighborhood divided by number of all possible connections.

LC(x)=\sum_{v \in N(x)}{\frac{|N(x) \cap N(v)|}{|N(x)|*(|N(x)|-1)}}

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

For further informations please refer to [Watts].

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.localClustering()
// Graph where each vertex is associated with its local clustering coefficient

You can also compute local clustering coefficient for graph treating it 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.localClustering(VertexMeasureConfiguration(treatAsUndirected=true))
// Graph where each vertex is associated with its local clustering coefficient computed for undirected graph

References:

[Watts]

Watts and Steven Strogatz, “Collective dynamics of ‘small-world’ networks”, Nature, vol. 393, pp 440-442, 1998 HTML