 TOPICS  # Graph Distance The distance between two vertices and of a finite graph is the minimum length of the paths connecting them (i.e., the length of a graph geodesic). If no such path exists (i.e., if the vertices lie in different connected components), then the distance is set equal to . In a grid graph the distance between two vertices is the sum of the "vertical" and the "horizontal" distances (right figure above).

The matrix consisting of all distances from vertex to vertex is known as the all-pairs shortest path matrix, or more simply, the graph distance matrix.

All-Pairs Shortest Path, Bellman-Ford Algorithm, Floyd-Warshall Algorithm, Dijkstra's Algorithm, Distance Graph, Girth, Graph Circumference, Graph Diameter, Graph Distance Matrix, Graph Geodesic, Shortest Path Problem

This entry contributed by Margherita Barile

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## References

Buckley, F. and Harary, F. Distance in Graphs. Redwood City, CA: Addison-Wesley, 1990.Diestel, R. Graph Theory, 3rd ed. New York: Springer-Verlag, p. 8, 1997.Wilson, R. J. Introduction to Graph Theory, 3rd ed. New York: Longman, p. 30, 1985.

Graph Distance

## Cite this as:

Barile, Margherita. "Graph Distance." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/GraphDistance.html