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v5.0
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    English
    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.

      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"}])
      

      Creating HDC Projection

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

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

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

      Parameters

      Algorithm name: graph_centrality

      Name
      Type
      Spec
      Default
      Optional
      Description
      ids []_id / / Yes Specifies nodes for computation by their _id; computes for all nodes if it is unset.
      uuids []_uuid / / Yes Specifies nodes for computation by their _uuid; computes for all nodes if it is unset.
      direction String in, out / Yes Specifies that the shortest paths shoud only contain incoming edges (in) or outgoing edges (out).
      return_id_uuid String uuid, id, both uuid Yes Includes _uuid, _id, or both to represent 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 the results by graph_centrality.

      File Writeback

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

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

      Result:

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

      DB Writeback

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

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

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

      Full Return

      CALL algo.graph_centrality("hdc_graph_centrality", {
        params: {
          return_id_uuid: "id",
          ids: ["A","B","C"],
          order: "asc"
        },
        return_params: {}
      }) YIELD gc
      RETURN gc
      

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

      Result:

      _id graph_centrality
      B 0.2
      C 0.2
      A 0.25

      Stream Return

      CALL algo.graph_centrality("hdc_graph_centrality", {
        params: {
          return_id_uuid: "id"
        },
        return_params: {type: "stream"}
      }) YIELD gc
      FILTER gc.graph_centrality > 0.25
      RETURN gc
      

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

      Result:

      _id graph_centrality
      E 0.333333
      F 0.333333
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