Communicability

graph-theory

Definition

Communicability

Communicability is a measures the ease or efficiency with which information can travel from vertex to vertex through the graph.

It is defined as the matrix exponential of the adjacency matrix:

where:

• represents the number of walks of length between vertices

• serves to weight walks of different lengths

  The element is the total communicability between vertex and , accounting for all possible walks of any length between them.

Understanding

The weighting factor ensures that longer walks contribute less to communicability, reflecting that information is more likely to travel through shorter, more direct routes.