Distance (graph theory)
Length of shortest path between two nodes of a graph / From Wikipedia, the free encyclopedia
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In the mathematical field of graph theory, the distance between two vertices in a graph is the number of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance.[1] Notice that there may be more than one shortest path between two vertices.[2] If there is no path connecting the two vertices, i.e., if they belong to different connected components, then conventionally the distance is defined as infinite.
In the case of a directed graph the distance d(u,v) between two vertices u and v is defined as the length of a shortest directed path from u to v consisting of arcs, provided at least one such path exists.[3] Notice that, in contrast with the case of undirected graphs, d(u,v) does not necessarily coincide with d(v,u)—so it is just a quasi-metric, and it might be the case that one is defined while the other is not.