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      HANP

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

      Overview

      The HANP (Hop Attenuation & Node Preference) algorithm extends the traditional Label Propagation algorithm (LPA) by incorporating a label score attenuation mechanism and considering the influence of neighbor node degree on neighbor label weight. The goal of HANP is to improve the accuracy and robustness of community detection in networks, it was proposed in 2009:

      Concepts

      Hop Attenuation

      HANP associates each label with a score which decreases as it propagates from its origin. All labels are initially given a score of 1. Each time a node adopts new label from its neighborhood, a new attenuated score would be assigned to this new label by subtracting the hop attenuation δ (0 < δ < 1).

      The hop attenuation mechanism limits the propagation of labels to nearby nodes and prevents them from spreading too broadly across the network.

      Node Preference

      In the calculation of the new maximal label, HANP incorporates node preference based on node degree. When node j ∈ Ni propagates its label L to node i, the weight of label L is calculated by:

      where,

      • sj(L) is the score of label L in j.
      • degj is the degree of j. When m > 0, more preference is given to node with high degree; m < 0, more preference is given to node with low degree; m = 0, no node preference is applied.
      • wij is the sum of edge weights between i and j.

      As the edge weights and label scores denoted in the example below, set m = 2 and δ = 0.2, the label of the blue node will be updated from d to a, and the score of label a in the blue node will be attenuated to 0.6.

      Considerations

      • HANP ignores the direction of edges but calculates them as undirected edges.
      • Node with self-loops propagates its current label(s) to itself, and each self-loop is counted twice.
      • When the selected label is equal to the current label, let δ = 0.
      • HANP follows the synchronous update principle when updating node labels. This means that all nodes update their labels simultaneously based on the labels of their neighbors. The label score mechanism can prevent label oscillations.
      • Due to factors such as the order of nodes, the random selection of labels with equal weights, and parallel calculations, the community division results of HANP may vary.

      Syntax

      • Command: algo(hanp)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      node_label_property @<schema>?.<property> Numeric/String type, must LTE / Yes Node property to initialize node labels, nodes without the property are not involved in label propagation; UUID is used as label for all nodes if not set
      edge_weight_property @<schema>?.<property> Numeric type, must LTE / Yes Edge property to use as edge weight
      m float / 0 Yes The power exponent of the degree of neighbor node: when m > 0, more preference is given to node with high degree; m < 0, more preference is given to node with low degree; m = 0, no node preference is applied
      delta float [0, 1] 0 Yes Hop attenuation δ
      loop_num int ≥1 5 Yes Number of propagation iterations
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results

      Examples

      The example graph is as follows, nodes are of schema user, edges are of schema connect, the value of @connect.strength is shown in the graph:

      File Writeback

      Spec Content
      filename _id,label_1,score_1
      algo(hanp).params({ 
        loop_num: 10,
        edge_weight_property: 'strength',
        m: 2, 
        delta: 0.2 
      }).write({
        file:{
          filename: 'hanp'
        }
      })
      

      Statistics: label_count = 4
      Results: File hanp

      O,13,-0.600000,
      N,6,-1.000000,
      M,6,-1.000000,
      L,13,-0.600000,
      K,13,-0.600000,
      J,1,-0.200000,
      I,1,-0.200000,
      H,1,-0.200000,
      G,1,-0.200000,
      F,14,-1.000000,
      E,6,-0.200000,
      D,6,-0.200000,
      C,6,-0.200000,
      B,6,-0.200000,
      A,6,-0.400000,
      

      Property Writeback

      Spec
      Content
      Write to
      Data Type
      property label_1,score_1 Node property Label: string,
      Label score: float
      algo(hanp).params({ 
        node_label_property: '@user.interest',
        m: 0.1, 
        delta: 0.3
      }).write({
        db:{
          property: 'lab'
        }
      })
      

      Statistics: label_count = 3
      Results: The label and label score of each node is written to new properties lab_1 and score_1

      Direct Return

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its label, label score _uuid, label_1, score_1
      1 KV Number of labels label_count
      algo(hanp).params({ 
        loop_num: 12,
        node_label_property: '@user.interest',
        m: 1,
        delta: 0.2
      }) as res, stats
      return res, stats
      

      Results: res and stats

      _uuid label_1 score_1
      15 movie -1.400000
      14 movie -0.400000
      13 saxophone -0.200000
      12 saxophone -0.200000
      11 saxophone -0.400000
      10 flute -0.200000
      9 flute -0.200000
      8 flute -0.200000
      7 flute -0.200000
      6 movie -0.400000
      5 movie -0.200000
      4 movie -0.200000
      3 movie -0.200000
      2 movie -0.200000
      1 movie -0.400000
      label_count
      3

      Stream Return

      Alias Ordinal
      Type
      Description
      Columns
      0 []perNode Node and its label, label score _uuid, label_1, score_1
      algo(hanp).params({ 
        loop_num: 12,
        node_label_property: '@user.interest',
        m: 1,
        delta: 0.2
      }).stream() as hanp
      group by hanp.label_1
      with count(hanp) as labelCount
      return table(hanp.label_1, labelCount) 
      order by labelCount desc
      

      Results: table(hanp.label_1, labelCount)

      hanp.label_1 labelCount
      movie 8
      flute 4
      saxophone 3

      Stats Return

      Alias Ordinal
      Type
      Description Columns
      0 KV Number of labels label_count
      algo(hanp).params({ 
        loop_num: 5,
        node_label_property: 'interest',
        m: 0.6,
        delta: 0.2
      }).stats() as count
      return count
      

      Results: count

      label_count
      5
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