Show how the clustering coefficient can be computed in a regular l…
Show how the clustering coefficient can be computed in a regular lattice of degree k.
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Technifi Expert’s Answer:
Clustering Coefficient : A measure of the degree to which nodes in a graph tend to cluster together. Global Clustering Coefficient: The ratio of the number of closed triplets to the number of all triplets.
Local Clustering Coefficient of a node in a graph quantifies how close its neighbours are to being a complete graph (clique).
A graph G=(V,E) formally consists of a set of vertices V and a set of edges E between them. An edge e connects vertex vi with vertex vj. The neighbourhood Ni for a vertex vi is defined as its immediately connects neighbours as follows:
We define ki as the number of vertices,Ni, in the neighbourhood, Ni, of a vertex
The local clustering coefficient Ci for a vertex CiVi is then given by the proportion of links between the vertices within its neighbourhood divided by the number of links that could possibly exist between them. For a directed graph, eij is distinct from eji, and therefore for each neighbourhood, N i there are ki(ki-1) links that could exist among the vertices within the neighbourhood ki is the number of neighbours of a vertex). Thus, the local clustering coefficient for directed graphs is given as
Thus, the local clustering coefficient for undirected graphs can be defined as
Where K is the degree of regular lattice
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