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v4.3
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    v4.3

      Preferential Attachment

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

      The Topological Link Prediction algorithm employs various metrics to assess the similarity between pairs of nodes, leveraging the topological attributes of nodes. A higher similarity score implies a greater likelihood of future connectivity between two nodes (which are not connected yet).

      Overview

      Preferential attachment is a common phenomenon in complex network where nodes with more connections are more likely to establish new connections. When both nodes possess a large number of connections, the probability of them forming a connection is significantly higher. This phenomenon was utilized by A. Barabási and R. Albert in their proposed BA model for generating random scale-free networks in 2002:

      The Preferential Attachment algorithm gauges the similarity between two nodes by calculating the product of the number of neighbors each node has. It is computed using the following formula:

      where N(x) and N(y) are the sets of adjacent nodes to nodes x and y respectively.

      Higher Preferential Attachment scores indicate greater similarity between nodes, while a score of 0 indicates no similarity between two nodes.

      In this example, PA(D,E) = |N(D)| * |N(E)| = |{B, C, E, F}| * |{B, D, F}| = 4 * 3 = 12.

      Considerations

      • The Preferential Attachment algorithm ignores the direction of edges but calculates them as undirected edges.

      Syntax

      • Command: algo(topological_link_prediction)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      ids / uuids []_id / []_uuid / / No ID/UUID of the first set of nodes to calculate; each node in ids/uuids will be paired with each node in ids2/uuids2
      ids2 / uuids2 []_id / []_uuid / / No ID/UUID of the second set of nodes to calculate; each node in ids/uuids will be paired with each node in ids2/uuids2
      type string Preferential_Attachment Adamic_Adar No Type of similarity; for Preferential Attachment, keep it as Preferential_Attachment
      limit int >=-1 -1 Yes Number of results to return, -1 to return all results

      Example

      The example graph is as follows:

      File Writeback

      Spec Content
      filename node1,node2,num
      algo(topological_link_prediction).params({
        uuids: [3],
        uuids2: [1,5,7],
        type: 'Preferential_Attachment'
      }).write({
        file:{ 
          filename: 'pa'
        }
      })
      

      Results: File pa

      C,A,3.000000
      C,E,6.000000
      C,G,3.000000
      

      Direct Return

      Alias Ordinal Type
      Description
      Columns
      0 []perNodePair Node pair and its similarity node1, node2, num
      algo(topological_link_prediction).params({
        ids: 'C',
        ids2: ['A','C','E','G'],
        type: 'Preferential_Attachment'
      }) as pa 
      return pa 
      

      Results: pa

      node1 node2 num
      3 1 3
      3 5 6
      3 7 3

      Stream Return

      Alias Ordinal Type
      Description
      Columns
      0 []perNodePair Node pair and its similarity node1, node2, num
      find().nodes() as n
      with collect(n._id) as nID
      algo(topological_link_prediction).params({
        ids: 'C',
        ids2: nID,
        type: 'Preferential_Attachment'
      }).stream() as pa
      where pa.num >= 2
      return pa
      

      Results: pa

      node1 node2 num
      3 2 12
      3 4 12
      3 5 6
      3 6 9
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