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v2.x
    v4.0

    Local Clustering Coefficient

      Advanced  

    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(<>)

    Configuration Item Type Default Value Specification Description
    ids []_id (All nodes) Ultipa ID The list of ID of nodes to be calculated
    uuids []_uuid (All nodes) Ultipa UUID The list of UUID of nodes to be calculated
    limit int -1 -1 or >=0 Number of results to return, -1 means to return all results
    order string / ASC or DESC, case insensitive To sort the retuned 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], limit: -1 })
    

    File Writeback

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

    Parameter Type Default Value Specification Description
    filename string / / Name of the file path to be written back. Columns of the file are: _idcentrality

    Property Writeback

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

    Parameter Type Default Value Specification Description
    property string / / Name of the node property to be written back. Write the local clustering coefficient back to: <property>

    Statistics Writeback

    (Not supported)

    Direct Return

    as <alias> return <alias>

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

    Streaming Return

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

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

    Real-time Statistics

    (Not supported)

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