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What does LocalClusteringCoefficient compute for directed graphs?

Posted 9 years ago

I have already asked this question on StackExchange.

What does LocalClusteringCoefficient compute for directed graphs?

For undirected graphs it follows the standard definitions and computes GraphDensity[Subgraph[g, AdjacencyList[g, v]]] for vertex v. I am not aware of a standard definition for directed graphs and I am unable to guess how the results it returns are computed. The documentation states that it does support directed graphs.

To take an example, can someone explain the result 1/2 for vertex 1 here?

g = Graph[{1, 2, 3, 4}, {1 -> 2, 2 -> 3, 3 -> 1, 1 -> 4}, 
  VertexLabels -> "Name"]

LocalClusteringCoefficient[g]
(* {1/2, 1, 1, 0} *)

What about 1/3 here?

g = Graph[{1, 2, 3, 4}, {1 -> 2, 2 -> 3, 3 -> 1, 1 -> 4, 4 -> 1}, 
  VertexLabels -> "Name"]

LocalClusteringCoefficient[g]
(* {1/3, 1, 1, 0} *)
POSTED BY: Szabolcs Horvát

I received a response from @Ilian Gachevski on StackExchange. It computes the cyclic clustering coefficient as defined on page 13 of this paper. Thank you!

POSTED BY: Szabolcs Horvát
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