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v4.3
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    v4.3

      Local Clustering Coefficient

      ✓ File Writeback ✓ Property Writeback ✓ Direct Return ✓ Stream Return ✕ Stats

      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:
      Name
      Type
      Spec
      Default
      Optional
      Description
      ids / uuids []_id / []_uuid / / Yes ID/UUID of nodes to calculate the local clustering coefficient, calculate for all nodes if not set
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results
      order string asc, desc / Yes Sort nodes by the value of the local clustering coefficient

      Examples

      The example graph is as follows:

      File Writeback

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

      Results: File lcc

      Lee,0.266667
      Choi,1
      

      Property Writeback

      Spec Content Write to Data Type
      property centrality Node property float
      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

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its local clustering coefficient _uuid, centrality
      algo(clustering_coefficient).params({
        order: 'desc'
      }) as lcc 
      return lcc
      

      Results: lcc

      _uuid centrality
      5 1
      2 1
      7 0.666667
      4 0.666667
      3 0.666667
      1 0.266667
      6 0

      Stream Return

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its local clustering coefficient _uuid, centrality
      algo(clustering_coefficient).params().stream() as lcc
      where lcc.centrality == 1
      return count(lcc)
      

      Results: 2

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