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      Degree Centrality

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

      Overview

      The Degree Centrality algorithm is used to find important nodes in the network, it measures the number of incoming and/or outgoing edges incident to the node, or the sum of weights of those edges. Degree is the simplest and most efficient graph algorithm since it only considers the 1-hop neighborhood of nodes. Degree plays a vital role in scientific computing, feature extraction, supernode recognition and other fields.

      Concepts

      In-Degree and Out-Degree

      The number of incoming edges a node has is called its in-degree; accordingly, the number of outgoing edges is called out-degree. If ignores edge direction, it is degree.

      In this graph, the red node has in-degree of 4 and out-degree of 3, and its degree is 7. Directed self-loop is regarded as an incoming edge and an outgoing edge.

      Weighted Degree

      In many applications, each edge of a graph has an associated numeric value, called weight. In weighted graph, weighted degree of a node is the sum of weights of all its neighbor edges. Unweighted degree is equivalent to when all edge weights are 1.

      In this weighted graph, the red node has weighted in-degree of 0.5 + 0.3 + 2 + 1 = 3.8 and weighted out-degree of 1 + 0.2 + 2 = 3.2, and its weighted degree is 3.2 + 3.8 = 7.

      Considerations

      • Degree of isolated node only depends on its self-loop. If it has no self-loop, degree is 0.
      • Every self-loop is counted as 2 edges attaching to its node. Directed self-loop is viewed as an incoming edge and an outgoing edge.

      Syntax

      • Command: algo(degree)
      • 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
      edge_schema_property []@<schema>?.<property> Numeric type, must LTE / Yes Edge property(-ies) to use as edge weight(s), where the values of multiple properties are summed up
      direction string in, out / Yes in for in-degree, out for out-degree
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results
      order string asc, desc / Yes Sort nodes by the size of degree

      Examples

      The example is a social network, edge property @follow.score can be used as weights:

      File Writeback

      Spec Content
      filename _id,degree
      algo(degree).params().write({
        file:{ 
          filename: 'degree_all'
        }
      })
      

      Statistics: total_degree = 20, average_degree = 2.25
      Results: File degree_all

      Tim,0
      Bill,1
      Bob,2
      Sam,2
      Joe,3
      Anna,5
      Cathy,4
      Mike,3
      

      Property Writeback

      Spec Content Write to Data Type
      property degree Node property double
      algo(degree).params({
        edge_schema_property: '@follow.score'
      }).write({
        db:{ 
          property: 'degree'
        }
      })
      

      Statistics: total_degree = 40.4, average_degree = 5.05
      Results: Degree for each node is written to a new property named degree, statistics is returned at the same time

      Direct Return

      Alias Ordinal
      Type
      Description Columns
      0 []perNode Node and its degree _uuid, degree
      1 KV Total and average degree of all nodes total_degree, average_degree
      algo(degree).params({ 
        edge_schema_property: '@follow.score',
        order: 'desc' 
      }) as degree, stats
      return degree, stats
      

      Results: degree and stats

      _uuid degree
      3 11.1
      2 6.5
      4 6.1
      6 5.2
      1 4.9
      5 4.3
      7 2.3
      8 0
      total_degree average_degree
      40.4 5.05

      Stream Return

      Alias Ordinal
      Type
      Description Columns
      0 []perNode Node and its degree _uuid, degree

      Example: Find 1-hop neighbors of the node with the highest degree, return all information of those neighbors

      algo(degree).params({
        order: 'desc',
        limit: 1 
      }).stream() as results
      khop().src({_uuid == results._uuid}).depth(1) as neighbors
      return neighbors{*}
      

      Results: neighbors

      _id _uuid
      Bill 7
      Sam 5
      Joe 4
      Cathy 2
      Mike 1

      Stats Return

      Alias Ordinal
      Type
      Description Columns
      0 KV Total and average degree of all nodes total_degree, average_degree
      algo(degree).params({
        direction: 'out'
      }).stats() as stats
      return stats
      

      Results: stats

      total_degree average_degree
      10 1.25
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