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Overview

After pairing all neighbors of a node, local clustering coefficient is the probability obtained by dividing the number of pairs which two nodes have edge in between by the number of all pairs.

Local clustering coefficient can be used to examine the tightness of the ego network of node. For example, in social network, it reveals how familiar the friends of one person are, which can help to distinguish the type of social group, such as relatives and friends, communities, agents, etc.

Basic Concept

Ego Network

Ego network is a subgraph formed by one center node (Ego) and all its 1-step neighbors (Alter). Please read the related content in Induced Subraph algorithm for the introduction to subgraph.

Specifying the red node in the graph above as Ego, its ego network contains the red node, the green nodes and all the red edges.

Local Clustering Coefficient

Local clustering coefficient is obtained by dividing the number of neighbor pairs of a node which two nodes have edge in between by the number of all neighbor pairs of that node.

x in the formula above represents the node to be calculated, i and j are any two distinct neighbors in x's ego network; δ(i,j) is 1 when there is edge between i and j, and 0 otherwise; k is the number of nodes in x's ego network, that is, (k-1)(k-2)/2 is the number of node pairs of i and j.

For the ego network of the red node in the graph above, only yellow-green and blue-purple node pairs have edge in between, thus the local clustering coefficient of the red node is 2 / 6 = 0.3333.

Special Case

Lonely Node, Disconnected Graph

Lonely node does not connect with any other node, its local clustering coefficient is 0, and it does not participate in the calculation of any local clustering coefficient.

Nodes in one connected component must not participate in the calculation of the local clustering coefficient of nodes in other connected components.

Self-loop Edge

Self-loop edge of a node does not increase the number of neighbors of the node.

Directed Edge

For directed edges, Local Clustering Coefficient algorithm ignores the direction of edges but calculates them as undirected edges.

Command

algo(clustering_coefficient).params(<>)

Example: Calculate the local clustering coefficient of nodes (UUID = 1,2,3)

algo(clustering_coefficient).params({ uuids: [1,2,3], limit: -1 })

File Writeback

.write({file: {<>}})

Property Writeback

.write({db: {<>}})

Statistics Writeback

(Not supported)

Direct Return

as <alias> return <alias>

Streaming Return

.stream() as <alias> return <alias>

Real-time Statistics

(Not supported)