The two most common measures of triadic closure for a graph are (in no particular order) the
clustering coefficient and transitivity for that graph.
Clustering coefficient One measure for the presence of triadic closure is
clustering coefficient, as follows: Let G = (V,E) be an undirected simple graph (i.e., a graph having no self-loops or multiple edges) with V the set of vertices and E the set of edges. Also, let N = |V| and M = |E| denote the number of vertices and edges in G, respectively, and let d_i be the
degree of vertex i. We can define a triangle among the triple of vertices i, j, and k to be a set with the following three edges: {(i,j), (j,k), (i,k)}. We can also define the number of triangles that vertex i is involved in as \delta (i) and, as each triangle is counted three times, we can express the number of triangles in G as \delta (G) = \frac{1}{3} \sum_{i\in V} \ \delta (i). Assuming that triadic closure holds, only two strong edges are required for a triple to form. Thus, the number of theoretical triples that should be present under the triadic closure hypothesis for a vertex i is \tau (i) = \binom{d_i}{2}, assuming d_i \ge 2. We can express \tau (G) = \frac{1}{3} \sum_{i\in V} \ \tau (i). Now, for a vertex i with d_i \ge 2, the
clustering coefficient c(i) of vertex i is the fraction of triples for vertex i that are closed, and can be measured as \frac{\delta (i)}{\tau (i)}. Thus, the
clustering coefficient C(G) of graph G is given by C(G) = \frac {1}{N_2} \sum_{i \in V, d_i \ge 2} c(i), where N_2 is the number of nodes with degree at least 2.
Transitivity Another measure for the presence of triadic closure is transitivity, defined as T(G) = \frac{3\delta (G)}{\tau (G)}. ==Causes and effects==