# clusteringCoef: Calculate clustering coefficient for an undirected graph In RBGL: An interface to the BOOST graph library

## Description

Calculate clustering coefficient for an undirected graph

## Usage

 `1` ```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

## 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'.

## Value

Clustering coefficient for graph `G`.

## Author(s)

Li Long [email protected]

## References

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

 ```1 2 3 4 5 6 7``` ```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) ```