The global clustering coefficient of a graph is the ratio of the number of closed trails
of length 3 to the number of paths of length two in .
Let
be the adjacency matrix of . The number of closed trails of length 3 is equal to three
times the number of triangles (i.e., graph cycles of length
3), given by
(1)
and the number of graph paths of length 2 is given
by
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