Consider a network representing a symmetrical relation, “communicates with” for a set of nodes. When a pair of nodes (say, u and v) is linked by an edge so that they can communicate directly without intermediaries, they are said to be adjacent. A set of edges linking two or more modes (u, v, w) such that u would like to communicate with w, using node v, then how many times node u uses node v to reach node w and how many shortest paths node u uses to reach node w. There can, of course, be more than one geodesic, linking any pair of nodes.
Consider a graph representing the symmetrical relation, "communicates with" for a set of people. When a pair of points is linked by an edge so that they can communicate directly without intermediaries, they are said to be adjacent. A set of edges linking two or more points (pi, pj, pk) such that pi is adjacent to pj and pj is adjacent to pk constitute a path from pi to pk. The shortest path linking a pair of points is called a geodesic. There can, of course, be more than one geodesic linking any pair of points.
A barely concealed mostly verbatim adaption of what can be found in Freeman (1980). Where Nm leaves the path of the original text the definition becomes nearly incomprehensible and mathematically unsound (although the definition of a path given by Freeman also leaves a bit to be desired).