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    English

      Adamic-Adar Index

      ✓ 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

      The Adamic-Adar Index (AA Index) is a node similarity metric named after its creators Lada Adamic and Eytan Adar. This index measures the potential connection strength between two nodes based on the shared neighbors they have in the graph.

      The underlying idea of the AA Index is that common neighbors with low degree provide more valuable information about the similarity between two nodes than common neighbors with high degrees. It is computed using the following formula:

      where N(u) is the set of nodes adjacent to u. For each common neighbor u of the two nodes, the AA Index first calculates the reciprocal of the logarithm of its degree |N(u)|, then sums up these reciprocal values for all common neighbors.

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

      In this example, N(D) ∩ N(E) = {B, F}, where 1log|N(B)| = 1log4 = 1.6610, 1log|N(F)| = 1log3 = 2.0959, thus AA(D,E) = 1.6610 + 2.0959 = 3.7569.

      Considerations

      • The AA Index 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 Adamic_Adar Adamic_Adar Yes Type of similarity; for AA Index, keep it as Adamic_Adar
      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]
      }).write({
        file:{ 
          filename: 'aa'
        }
      })
      

      Results: File aa

      C,A,1.660964
      C,E,3.321928
      C,G,2.095903
      

      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: 'Adamic_Adar'
      }) as aa 
      return aa 
      

      Results: aa

      node1 node2 num
      3 1 1.66096404744368
      3 5 3.32192809488736
      3 7 2.09590327428938

      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
      }).stream() as aa
      where aa.num >= 2
      return aa
      

      Results: aa

      node1 node2 num
      3 4 3.75686732173307
      3 5 3.32192809488736
      3 7 2.09590327428938
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