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v5.0
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    v5.0

      k-Core

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

      Overview

      The k-Core algorithm identifies the maximal connected subgraph where all nodes have a minimum degree of k. It is commonly employed to extract closely connected groups in a graph for further analysis. The algorithm is widely utilized in various research domains including financial risk control, social network analysis, and biology. One of the key advantages of the k-Core algorithm is its low time complexity (linear), making it efficient for large-scale graph processing. Additionally, the resulting subgraphs have good intuitive interpretability, aiding in the understanding of the graph's structural patterns and relationships.

      The commonly accepted concept of k-core was first proposed by Seidman:

      Concepts

      k-Core

      The k-core of a graph is obtained through an iterative pruning process. Starting with the original graph, nodes with a degree less than k are successively removed until only nodes with degrees greater than or equal to k remain.

      Below is the pruning process to get the 3-core of the graph. In the first round, nodes {a, d, f} with degree less than 3 are removed , which then affects the removal of node b in the second round. After the second round, all remaining nodes have a degree of at least 3. Therefore, the pruning process ends, and the 3-core of this graph is induced by nodes {c, e, g, h}.

      Ultipa's k-Core algorithm identifies the k-core in each connected component.

      Considerations

      • The k-Core algorithm ignores self-loops in the graph. Any self-loop present is not considered when calculating the degree of the respective node.
      • The k-Core algorithm ignores the direction of edges but calculates them as undirected edges.

      Syntax

      • Command: algo(k_core)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      k int ≥1 / No Each node in the k-core has a degree that is equal to or greater than k

      Examples

      The example graph is as follows:

      File Writeback

      Spec
      Content
      Description
      filename _id ID of node in the k-core
      algo(k_core).params({
        k: 3
      }).write({
        file:{
          filename: '3-core'
        }
      })
      

      Results: File 3-core

      G
      F
      E
      D
      

      Direct Return

      Alias Ordinal
      Type
      Description
      0 []perNode UUIDs of nodes in the k-core
      algo(k_core).params({
        k: 2
      }) as k2 
      return k2
      

      Results: k2

      7
      6
      5
      4
      2
      3

      Stream Return

      Alias Ordinal
      Type
      Description
      0 []perNode UUIDs of nodes in the k-core
      algo(k_core).params({
        k: 2
      }).stream() as k2 
      find().nodes(k2) as nodes
      return nodes{*}
      

      Results: nodes

      _id _uuid
      G 7
      F 6
      E 5
      D 4
      C 2
      B 3
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