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v4.5
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    English
    v4.5

      HITS

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

      Overview

      The HITS (Hyperlink-Induced Topic Search) algorithm was developed by L.M. Kleinberg in 1999 with the purpose of improving the quality of search methods on the World Wide Web (WWW). HITS makes use of the mutual reinforcing relationship between authorities and hubs to evaluate and rank a set of linked entities.

      Concepts

      Authority and Hub

      In WWW, hyperlinks represent some latent human judgment: the creator of page p, by including a link to page q, has in some measure conferred authority on q. Instructively, a node with large in-degree is viewed as an authority.

      If a node points to considerable number of authoritative nodes, it is referred to as a hub.

      As illustrated in the graph below, red nodes are good authorities, green nodes are good hubs.

      Hubs and authorities exhibit what could be called a mutually reinforcing relationship: a good hub points to many good authorities; a good authority is pointed to by many good hubs.

      Compute Authorities and Hubs

      HITS algorithm operates on the whole graph iteratively to compute the authority weight (denoted as x) and hub weight (denoted as y) for each node through the link structure. Nodes with larger x-values and y-values are viewed as better authorities and hubs respectively.

      In a directed graph G = (V, E), all nodes are initialized with x = 1 and y = 1. In each iteration, for each node p ∈ V, update its x and y values as follows:

      Here is an example:

      At the end of one iteration, normalize all x values and all y values to meet the invariant below:

      The algorithm continues until the change of all x values and y values converges to within some tolerance, or the maximum iteration rounds is met. In the experiments of the original author, the convergence is quite rapid, 20 iterations are normally sufficient.

      Considerations

      • In HITS algorithm, self-loops are ignored.
      • Authority weight of nodes with no in-links is 0, hub weight of nodes with out-links is 0.

      Syntax

      • Command: algo(hits_centrality)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      max_loop_num int >=1 20 Yes Maximum rounds of iterations; the algorithm ends after running for all rounds, even though the condition of tolerance is not met
      tolerance float (0,1) 0.001 Yes When all authority weights and hub weights change less than the tolerance between iterations, the result is considered stable and the algorithm ends
      limit int ≥-1 -1 Yes Number of results to return, -1 to return all results

      Examples

      The example graph is as follows:

      File Writeback

      Spec Content
      filename _id,authority,hub
      algo(hits_centrality).params({}).write({
        file: {
          filename: 'rank'
        }
      })
      

      Results: File rank

      H,0.000000,0.000000
      G,0.213196,0.190701
      F,0.426420,0.000000
      E,0.000000,0.476726
      D,0.000000,0.572083
      C,0.000000,0.476726
      B,0.213196,0.381382
      A,0.852796,0.190701
      

      Property Writeback

      Spec Content Write to Data Type
      authority authority Node property double
      hub hub Node property double
      algo(hits_centrality).params({
        max_loop_num: 20,
        tolerance: 0.0001
      }).write({
        db: {
          authority: 'auth',
          hub: 'hub'
        }
      })
      

      Results: Authority weight for each node is written to a new property named auth, hub weight for each node is written to a new property named hub

      Direct Return

      Alias Ordinal
      Type
      Description Columns
      0 []perNode Node and its authority and hub weight _uuid, authority, hub
      algo(hits_centrality).params() as rank
      return rank
      

      Results: rank

      _uuid authority hub
      8 3.20199049138017e-11 0
      7 0.213196444093741 0.190700611234451
      6 0.426419530029166 1.43197368054726e-11
      5 0 0.476726292571473
      4 0 0.572082555485605
      3 0 0.476726292571473
      2 0.213196444093741 0.381381944251153
      1 0.852795952652963 0.190700611234451

      Stream Return

      Alias Ordinal
      Type
      Description Columns
      0 []perNode Node and its authority and hub weight _uuid, authority, hub
      algo(hits_centrality).params({
        max_loop_num: 20,
        tolerance: 0.0001
      }).stream() as rank
      find().nodes({_uuid == rank._uuid}) as nodes
      order by rank.hub desc
      return table(nodes._id, rank.hub)
      

      Results: table(nodes._id, rank.hub)

      nodes._id rank.hub
      D 0.572082555485605
      E 0.476726292571473
      C 0.476726292571473
      B 0.381381944251153
      G 0.190700611234451
      A 0.190700611234451
      F 1.43197368054726e-11
      H 0
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