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      k-Edge Connected Components

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

      Overview

      The k-Edge Connected Components algorithm aims to find groups of nodes that have strong interconnections based on their edges. By considering the connectivity of edges rather than just the nodes themselves, the algorithm can reveal clusters or communities within the graph where nodes are tightly linked to each other. This information can be valuable for various applications, including social network analysis, web graph analysis, biological network analysis, and more.

      Related material of the algorithm:

      Concepts

      Edge Connectivity

      The edge connectivity of a graph is a measure that quantifies the minimum number of edges that need to be removed in order to disconnect the graph or reduce its connectivity. It represents the resilience of a graph against edge failures. Given a graph G = (V, E), G is k-edge connected if it remains connected after the removal of any k-1 or fewer edges from G.

      The edge connectivity can also be interpreted as the maximum number of edge-disjoint paths between any two nodes in the graph. If the edge connectivity of a graph is k, it means that there are k edge-disjoint paths between any pair of nodes in the graph.

      Below shows a 3-edge connected graph and the edge-disjoint paths between each node pair.

      Edge-disjoint paths are paths that do not have any edge in common.

      k-Edge Connected Components

      Instead of determining whether the entire graph G is k-edge connected, the k-Edge Connected Components algorithm is interested in finding the maximal subsets of nodes Vi ⊆ V, where the subgraphs induced by Vi are k-edge connected.

      For example, in social networks, finding a group of people who are strongly connected is more important than computing the connectivity of the entire social network.

      Considerations

      • For k = 1, this problem is equivalent to finding the connected components of G.
      • The k-Edge Connected Component algorithm ignores the direction of edges but calculates them as undirected edges.

      Syntax

      • Command: algo(kcc)
      • Parameters:
      Name
      Type
      Spec
      Default
      Optional
      Description
      k int >1 / No There are k edge-disjoint paths between any pair of nodes in the k-edge connected components

      Examples

      The example graph is as follows:

      File Writeback

      Spec
      Content
      Description
      filename _id,_id,... The IDs of nodes that are contained in each k-edge connected component
      algo(kcc).params({
        k: 3
      }).write({
        file:{
          filename: 'result'
        }
      })
      

      Results: File result

      F,G,I,H,
      J,K,M,L,
      
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