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v4.3
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    v4.3

      Resource Allocation

      ✓ 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 Resource Allocation algorithm operates under the assumption that nodes transmit resources to each other through their shared neighbors, who act as transmitters. In its basic form, we consider each transmitter possessing a single unit of resource, which is evenly distributed among its neighbors. Consequently, the similarity between two nodes can be gauged by the magnitude of resources that one node transmits to the other. This concept was introduced by Tao Zhou, Linyuan Lü, and Yi-Cheng Zhang in 2009:

      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 Resource Allocation first calculates the reciprocal of its degree |N(u)|, then sums up these reciprocal values for all common neighbors.

      Higher Resource Allocation 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}, RA(D,E) = 1|N(B)| + 1|N(F)| = 14 + 13 = 0.5833.

      Considerations

      • The Resource Allocation 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 Resource_Allocation Adamic_Adar No Type of similarity; for Resource Allocation, keep it as Resource_Allocation
      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: 'Resource_Allocation'
      }).write({
        file:{ 
          filename: 'ra'
        }
      })
      

      Results: File ra

      C,A,0.250000
      C,E,0.500000
      C,G,0.333333
      

      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: 'Resource_Allocation'
      }) as ra 
      return ra 
      

      Results: ra

      node1 node2 num
      3 1 0.25
      3 5 0.5
      3 7 0.333333333333333

      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: 'Resource_Allocation'
      }).stream() as ra
      where ra.num >= 0.3
      return ra
      

      Results: ra

      node1 node2 num
      3 4 0.583333333333333
      3 5 0.5
      3 7 0.333333333333333
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