An idea closely related to the average degree of

Chapter 6, Problem 12

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An idea closely related to the average degree of separation in a graph is that of clustering. The global clustering coefficient for a given graph is given by C = 3 * T t where T = the number of triangles in the graph and t = the number of connected node triples. A connected node triple is a center node adjacent to an unordered pair of other nodes. For example, in the graph of Exercise 2, 345 (or 543) and 456 (654) are two such triples. Nodes that make up a triangle demonstrate transitivity; if a is adjacent to b and b is adjacent to c, then a is adjacent to c. Therefore c is a ratio of nodes in a transitive threesome to all nodes in a threesome. (One might think of this in terms of a social network as the probability that if you are a friend of mine and x is a friend of yours, then x is also a friend of mine.) a. Consider the graph in Figure 6.28 and the graph for Exercise 2. Which do you think has the higher clustering coefficient? b. Compute the clustering coefficient for the graph in Figure 6.28 c. Compute the clustering coefficient for the graph for Exercise 2

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