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    English

      Graph Centrality

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

      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.

      Syntax

      • Command: algo(graph_centrality)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      ids / uuids []_id / []_uuid / / Yes ID/UUID of the nodes to calculate, calculate for all nodes if not set
      direction string in, out / Yes Direction of all edges in the shortest path, in for incoming direction, out for outgoing direction
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results
      order string asc, desc / Yes Sort nodes by the centrality score

      Examples

      The example graph is as follows:

      File Writeback

      Spec Content
      filename _id,centrality
      algo(graph_centrality).params().write({
        file:{ 
          filename: 'res'
        }
      })
      

      Results: File res

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

      Property Writeback

      Spec Content Write to Data Type
      property centrality Node property float
      algo(graph_centrality).params().write({
        db:{ 
          property: 'gc'
        }
      })
      

      Results: Centrality score for each node is written to a new property named gc

      Direct Return

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its centrality _uuid, centrality
      algo(graph_centrality).params({
        ids: ['A', 'B', 'C'],
        order: 'asc'
      }) as gc
      return gc
      

      Results: gc

      _uuid centrality
      2 0.2
      3 0.2
      1 0.25

      Stream Return

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its centrality _uuid, centrality
      algo(graph_centrality).params().stream() as gc
      where gc.centrality > 0.25
      return gc
      

      Results: gc

      _uuid centrality
      6 0.333333
      5 0.333333
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