Measuring Degree of Relationship Clustering

How tight or loose are the relationships in a cluster? In a hybrid or mixed graph we define a clustering coefficient, C. To calculate C, list all the neighbors of a vertex, count the edges that link to its neighbors, and then divide the sum by the maximum number of edges that could possibly exist among the neighbors. Now repeat this operation for all the vertices and take the average. In contrast with the path length L, the clustering coefficient C stays large until the rewiring probability becomes rather large. Hence, over a wide range of p values, local connections dominate the graph between nearby nodes, but just a few shortcuts, like freeways connecting densely populated cities, may suffice for efficient long-distance connections.

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