RBGL (version 1.48.1)

clusteringCoef: Calculate clustering coefficient for an undirected graph

Description

Calculate clustering coefficient for an undirected graph

Usage

clusteringCoef(g, Weighted=FALSE, vW=degree(g))

Arguments

g

an instance of the graph class

Weighted

calculate weighted clustering coefficient or not

vW

vertex weights to use when calculating weighted clustering coefficient

Value

Clustering coefficient for graph G.

Details

For an undirected graph G, let delta(v) be the number of triangles with v as a node, let tau(v) be the number of triples, i.e., paths of length 2 with v as the center node.

Let V' be the set of nodes with degree at least 2.

Define clustering coefficient for v, c(v) = (delta(v) / tau(v)).

Define clustering coefficient for G, C(G) = sum(c(v)) / |V'|, for all v in V'.

Define weighted clustering coefficient for g, Cw(G) = sum(w(v) * c(v)) / sum(w(v)), for all v in V'.

References

Approximating Clustering Coefficient and Transitivity, T. Schank, D. Wagner, Journal of Graph Algorithms and Applications, Vol. 9, No. 2 (2005).

See Also

clusteringCoefAppr, transitivity, graphGenerator

Examples

con <- file(system.file("XML/conn.gxl",package="RBGL"))
g <- fromGXL(con)
close(con)
cc <- clusteringCoef(g)
ccw1 <- clusteringCoef(g, Weighted=TRUE)
vW  <- c(1, 1, 1, 1, 1,1, 1, 1)
ccw2 <- clusteringCoef(g, Weighted=TRUE, vW)