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v4.0
    v4.0

    Local Clustering Coefficient

    Overview

    Local clustering coefficient of a node refers to the probability that the neighbours of the node are also connected.

    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 Induced Subgraph 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 of a node is obtained by dividing the number of its neighbor pairs which have edge in between by the number of all neighbor pairs:

    where x represents the node to be calculated, i and j are any two distinct neighbors in the ego network of x; 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, (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, the Local Clustering Coefficient algorithm ignores the direction of edges but calculates them as undirected edges.

    Results and Statistics

    Take the 7-user social network graph below as an example, run the Local Clustering Coefficient algorithm:

    Algorithm results: Calculate local clustering coefficient for user Lee (UUID = 1) and Choi (UUID = 2), return _id, centrality or _uuid, centrality according to the execution method

    _uuid _id centrality
    1 Lee 0.26666668
    2 Choi 1.0000000

    Algorithm statistics: N/A

    Command and Configuration

    • Command: algo(clustering_coefficient)
    • Configurations for the parameter params():
    Name Type
    Default
    Specification
    Description
    ids / uuids []_id / []_uuid / / IDs or UUIDs of nodes to be calculated; all nodes to be calculated if not set
    limit int -1 >=-1 Number of results to return; return all results if sets to -1 or not set
    order string / ASC or DESC, case insensitive To sort the returned results; no sorting is applied if not set

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

    algo(clustering_coefficient).params({ 
      uuids: [1,2,3] 
    }) as lcc 
    return lcc
    

    Algorithm Execution

    Task Writeback

    1. File Writeback

    Configuration Data in Each Row
    filename _id,centrality

    Example: Calculate the local clustering coefficient of user Lee and Choi, write the algorithm results back to file named centrality

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

    2. Property Writeback

    Configuration Writeback Content Type Data Type
    property centrality Node property float

    Example: Calculate the local clustering coefficient of user Lee and Choi, write the algorithm results back to node property named lcc

    algo(clustering_coefficient).params({ 
      ids: ["Lee", "Choi"]
    }).write({
      db:{
        property: "lcc"
     }
    })
    

    3. Statistics Writeback

    This algorithm has no statistics.

    Direct Return

    Alias Ordinal
    Type
    Description Column Name
    0 []perNode Node and its local clustering coefficient _uuid, centrality

    Example: Calculate the local clustering coefficient of all nodes, define algorithm results as alias named results, and return the results

    algo(clustering_coefficient).params() as results 
    return results
    

    Streaming Return

    Alias Ordinal
    Type
    Description Column Name
    0 []perNode Node and its local clustering coefficient _uuid, centrality

    Example: Calculate the local clustering coefficient of all nodes, define algorithm results as alias named results, and return the results with local clustering coefficient other than 0

    algo(clustering_coefficient).params().stream() as results
    where results.centrality > 0
    return results
    

    Real-time Statistics

    This algorithm has no statistics.

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