vertexEmbeddedness.rst

Vertex Embeddedness

Is an average embededdness of neighbours of given vertex.

VE(x)=\frac{1}{|N(x)|}\sum_{v \in N(x)}{\frac{|N(x) \cap N(v)|}{|N(x) \cup N(v)|}}

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

For further informations please refer to [Dong].

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.vertexEmbeddedness()
// Graph where each vertex is associated with its vertex embeddedness

You can also compute vertex embeddedness 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.vertexEmbeddedness(VertexMeasureConfiguration(treatAsUndirected=true))
// Graph where each vertex is associated with its vertex embeddedness computed for undirected graph

References:

[Dong]

Dong, Y., Yang, Y., Tang, J., Yang, Y., & Chawla, N. V. (2014, August). Inferring user demographics and social strategies in mobile social networks. In Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (pp. 15-24). ACM. PDF