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    English

      Triangle Counting

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

      Overview

      The Triangle Counting algorithm identifies triangles in a graph, where a triangle represents a set of three nodes that are connected to each other. Triangles are important in graph analysis as they reflect the presence of loops or strong connectivity patterns within the graph.

      Triangles in social networks indicate the presence of cohesive communities. Identifying triangles helps in understanding the clustering and interconnectedness of individuals or groups within the network. In financial networks or transaction networks, the presence of triangles can be indicative of suspicious or fraudulent activities. Triangle counting can help identify patterns of collusion or interconnected transactions that might require further investigation.

      Concepts

      Triangle

      In a complex graph, it is possible for multiple edges to exist between two nodes. This can lead to the formation of more than one triangle involving three nodes. Take the graph below as an example:

      • Counting triangles assembled by edges, there are 4 different triangles.
      • Counting triangles assembled by nodes, there are 2 different triangles.

      The number of triangles assembled by edges tends to be greater than those assembled by nodes in complex graph. The choice of assembly principle should align with the objectives of the analysis and the insights sought from the graph data. In social network analysis, where the focus is often on understanding connectivity patterns among individuals, the assembling by node principle is commonly adopted. In financial network analysis or other similar domains, the assembling by edge principle is often preferred. Here, the emphasis is on the relationships between nodes, such as financial transactions or interactions. Assembling triangles based on edges allows for the examination of how tightly nodes are connected and how funds or information flow through the network.

      Considerations

      • The Triangle Counting algorithm ignores the direction of edges but calculates them as undirected edges.

      Syntax

      • Command: algo(triangle_counting)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      type int 1, 2 1 Yes 1 to assemble triangles by edges, 2 to assemble triangles by nodes
      result_type int 1, 2 1 Yes 1 to return the number of triangles, 2 to return triangles in the form of nodes or edges
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results

      Examples

      The example graph is as follows:

      File Writeback

      Spec
      Content
      filename edge1,edge2,edge3 or node1,node2,node3
      algo(triangle_counting).params({
        type: 1,
        result_type: 2
      }).write({
        file:{
          filename: "te"
      }})
      

      Statistics: triangle_count = 3
      Results: File te

      103,104,101
      103,104,102
      105,104,106
      
      algo(triangle_counting).params({
        type: 2,
        result_type: 2
      }).write({
        file:{
          filename: "tn"
      }})
      

      Statistics: triangle_count = 2
      Results: Files tn

      C4,C2,C1
      C3,C2,C1
      

      Direct Return

      Alias Ordinal
      Type
      Description Columns
      0 KV or []perTriangle Number of triangles or triangles triangle_count or edge1, edge2, edge3 or node1, node2, node3
      algo(triangle_counting).params({
        result_type: 1
      }) as count 
      return count
      

      Results: count

      triangle_count
      3
      algo(triangle_counting).params({
        result_type: 2
      }) as triangles 
      return triangles
      

      Results: triangles

      edge1 edge2 edge3
      103 104 101
      103 104 102
      105 104 106

      Stream Return

      Alias Ordinal
      Type
      Description Columns
      0 KV or []perTriangle Number of triangles or triangles triangle_count or edge1, edge2, edge3 or node1, node2, node3
      algo(triangle_counting).params({
        type: 2, 
        result_type:2 
      }).stream() as t
      call {
        with t
        find().nodes({_uuid in [t.node1, t.node2, t.node3]}) as nodes
        return sum(nodes.amount) as sumAmount
      }
      return table(t.node1, t.node2, t.node3, sumAmount)
      

      Results: table(t.node1, t.node2, t.node3, sumAmount)

      t.node1 t.node2 t.node3 sumAmount
      4 2 1 12
      3 2 1 9
      algo(triangle_counting).params({
        type: 2, 
        result_type:1
      }).stream() as tNodes 
      algo(triangle_counting).params({
        type: 1, 
        result_type:1
      }).stream() as tEdges
      return table(tNodes.triangle_count, tEdges.triangle_count)
      

      Results: table(tNodes.triangle_count, tEdges.triangle_count)

      tNodes.triangle_count tEdges.triangle_count
      2 3

      Stats Return

      Alias Ordinal Type
      Description
      Columns
      0 KV Number of triangles triangle_count
      algo(triangle_counting).params({
        result_type: 1
      }).stats() as sta 
      return sta
      

      Results: sta

      triangle_count
      3
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