Network Local Clustering Coefficient

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Network Local Clustering Coefficient

This metric is not implemented in any version. You can report this as a Bug.



The Network Local Clustering Coefficient is the average distribution of the Local Clustering Coefficient of all nodes in the network.

Objective

The Network Local Clustering Coefficient considers the Local Clustering Coefficient of each node in the network and calculates the mean of all nodes. The measure is standardized on the network size.

This measure can be used to show the average strength of connectedness between the nodes of the network.

Calculation

\bar{C} = \frac{1}{n}\sum_{i=1}^{n} C_i, where C_i \,\! is the Local Clustering Coefficient of node n_i\,\!.[1]

The result of this calculation is a number between 0 and 1, with 1 meaning all nodes are connected to each other.

This measure can not be calculated on a network with isolated nodes.

Statement

R-example
library(igraph)

g <- random.graph.game(10, 3/10)
sum(transitivity(g, type="local"))/vcount(g)

// if you network contains different components
cl <- clusters(g)
subg <- subgraph(g, which(cl$membership == which.max(cl$csize)-1)-1)
sum(transitivity(subg, type="local"))/vcount(subg)

Notice: This measure can not be calculated on a network with isolated nodes and returns the value NaN. For that case you can rerun the statement to build the network (g <- random.graph.game(10, 3/10)).

Reference

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