Local Clustering Coefficient

Overview

The Local Clustering Coefficient algorithm calculates the density of connection among the immediate neighbors of a node. It quantifies the ratio of actual connections among the neighbors to the maximum possible connections.

The local clustering coefficient provides insights into the cohesion of a node's ego network. In the context of a social network, the local clustering coefficient helps understand the degree of interconnectedness among an individual's friends or acquaintances. A high local clustering coefficient suggests that the person's friends are likely to be connected to each other, indicating the presence of a closely-knit social group, such as a family. Conversely, a low local clustering coefficient indicates a more dispersed or loosely interconnected ego network, where the person's friends do not have strong connections with each other.

Concepts

Local Clustering Coefficient

Mathematically, the local clustering coefficient of a node in an undirected graph is calculated as the ratio of the number of connected neighbor pairs to the total number of possible neighbor pairs:

where n is the number of nodes contained in the 1-hop neighborhood of node v (denoted as N(v)), i and j are any two distinct nodes within N(v), δ(i,j) is equal to 1 if i and j are connected, and 0 otherwise.

In this example, the local clustering coefficient of the red node is 1/(5*4/2) = 0.1.

Considerations

• The Local Clustering Coefficient algorithm ignores the direction of edges but calculates them as undirected edges.

Syntax

• Command: algo(clustering_coefficient)
• Parameters:

Examples

The example graph is as follows:

File Writeback

algo(clustering_coefficient).params({ 
  ids: ['Lee', 'Choi']
}).write({
  file:{
    filename: 'lcc'
 }
})

Results: File lcc

Lee,0.266667
Choi,1

Property Writeback

algo(clustering_coefficient).params().write({
  db:{
    property: 'lcc'
 }
})

Results: The value of the local clustering coefficient for each node is written to a new property named lcc

Direct Return

algo(clustering_coefficient).params({
  order: 'desc'
}) as lcc 
return lcc

Results: lcc

Stream Return

algo(clustering_coefficient).params().stream() as lcc
where lcc.centrality == 1
return count(lcc)

Results: 2