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v5.0
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    v5.0

      Graph Centrality

      HDC

      Overview

      Graph centrality of a node is measured by the maximum shortest distance from the node to all other reachable nodes. This measurement, along with other measurements like closeness centrality and graph diameter, can be considered jointly to determine whether a node is literally located at the very center of the graph.

      Graph centrality takes on values between 0 to 1, nodes with higher scores are closer to the center.

      Concepts

      Shortest Distance

      The shortest distance of two nodes is the number of edges contained in the shortest path between them. Please refer to Closeness Centrality for more details.

      Graph Centrality

      Graph centrality score of a node defined by this algorithm is the inverse of the maximum shortest distance from the node to all other reachable nodes. The formula is:

      where x is the target node, y is any node that connects with x along edges (x itself is excluded), d(x,y) is the shortest distance between x and y.

      In this graph, the green number and red number next to each node is the shortest distance between the node and the green node and red node. Graph centrality scores of the green and red nodes are 1/4 = 0.25 and 1/3 = 0.3333 respectively.

      Regarding closeness centrality, the green node has score 8/(1+1+1+1+2+3+4+3) = 0.5, the red node has score 8/(3+3+3+2+1+1+2+1) = 0.5. When two nodes have the same closeness centrality score, graph centrality can be viewed as the subsidiary basis to determine which node is closer to the center.

      Considerations

      • The graph centrality score of isolated nodes is 0.
      • The Graph Centrality algorithm ignores the direction of edges but calculates them as undirected edges.

      Parameters

      Name
      Type
      Spec
      Default
      Optional
      Description
      project String / / / The projection on which the algorithm will run. This is required for writeback modes but not applicable to return modes.
      ids []_id / / Yes Specifies nodes by their _id values for computation; computes for all nodes if it is unset.
      uuids []_uuid / / Yes Specifies nodes by their _uuid values for computation; computes for all nodes if it is unset.
      direction String in, out / Yes Specifies direction of edges in each shortest path, with in for incoming direction, out for outgoing direction; ignores direction if not set.
      return_id_uuid String uuid, id, both uuid Yes Includes _uuid, _id, or both values for nodes in the results.
      limit Integer ≥-1 -1 Yes Limits the number of results returned; -1 includes all results.
      order String asc, desc / Yes Sorts nodes by their centrality scores.

      Example Graph

      To create this graph:

      // Runs each row separately in order in an empty graphset
      create().node_schema("user").edge_schema("vote")
      insert().into(@user).nodes([{_id:"A"},{_id:"B"},{_id:"C"},{_id:"D"},{_id:"E"},{_id:"F"},{_id:"G"},{_id:"H"},{_id:"I"},{_id:"J"}])
      insert().into(@vote).edges([{_from:"A", _to:"B"}, {_from:"A", _to:"C"}, {_from:"A", _to:"D"}, {_from:"E", _to:"A"}, {_from:"E", _to:"F"}, {_from:"F", _to:"G"}, {_from:"F", _to:"I"}, {_from:"G", _to:"H"}, {_from:"H", _to:"I"}])
      

      Running on HDC Projections

      Creating HDC Projections

      To project the entire graph to the HDC server hdc-server-1 as hdc_graph_centrality:

      hdc.graph.create("hdc_graph_centrality", {
        nodes: {"*": ["*"]},
        edges: {"*": ["*"]},
        direction: "undirected",
        load_id: true,
        update: "static",
        query: "query",
        default: true
      }).to("hdc-server-1")
      

      File Writeback

      algo(graph_centrality).params({
        project: "hdc_graph_centrality",
        return_id_uuid: "id"
      }).write({
        file: {
          filename: "graph_centrality"
        }
      })
      

      Results:

      _id,graph_centrality
      C,0.2
      I,0.25
      G,0.25
      A,0.25
      E,0.333333
      J,0
      D,0.2
      F,0.333333
      H,0.2
      B,0.2
      

      DB Writeback

      Writes the graph_centrality values from the results to the specified node property. The property type is float.

      algo(graph_centrality).params({
        project: "hdc_graph_centrality"
      }).write({
        db:{ 
          property: 'gc'
        }
      })
      

      Full Return

      exec{
        algo(graph_centrality).params({
          return_id_uuid: "id",
          ids: ["A","B","C"],
          order: "asc"
        }) as r
        return r
      } on hdc_graph_centrality
      

      Results:

      _id graph_centrality
      B 0.2
      C 0.2
      A 0.25

      Stream Return

      exec{
        algo(graph_centrality).params({
          return_id_uuid: "id"
        }).stream() as gc
        where gc.graph_centrality > 0.25
        return gc
      } on hdc_graph_centrality
      

      Results:

      _id graph_centrality
      E 0.333333
      F 0.333333
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