Math Insight

Definition of the transitivity of a graph


The transitivity $T$ of a graph is based on the relative number of triangles in the graph, compared to total number of connected triples of nodes. \begin{gather*} T = \frac{3 \times \text{number of triangles in the network}}{\text{number of connected triples of nodes in the network}}. \end{gather*} The factor of three in the number accounts for the fact that each triangle contributes to three different connected triples in the graph, one centered at each node of the triangle. With this definition, $0 \le T \le 1$, and $T=1$ if the network contains all possible edges.

The transitivity of a graph is closely related to the clustering coefficient of a graph, as both measure the relative frequency of triangles.