A graph geodesic is a shortest path between two graph vertices 
of a graph (Skiena 1990, p. 225). There may be more
than one different shortest paths, all of the same length. Graph geodesics may be
found using a breadth-first traversal
(Moore 1959) or using Dijkstra's algorithm
(Skiena 1990, p. 225). One (of possibly several) graph geodesics of a graph
from vertex 
to vertex 
can be found in the Wolfram
Language using FindShortestPath[g,
u, v]. The length of the graph geodesic between these points 
is called the graph distance
between 
and 
.
The length of the maximum geodesic in a given graph is called the graph diameter, and the length of the minimum geodesic is called the graph radius.
The matrix 
consisting of all graph distances from vertex 
to vertex 
is known as the all-pairs shortest path matrix, or more
simply, the graph distance matrix.
A graph which possesses a unique geodesic between every pair of vertices is known as a geodetic graph.
