Locating Central Paths in a Graph

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Abstract
Concepts which measure the centrality of a vertex in a graph (eccentricity, distance and branch weight) are extended to paths in a graph. Locating paths with minimum eccentricity and distance, respectively, may be viewed as multicenter and multimedian problems, respectively, where the facilities are located on vertices that must constitute a path. The third problem is to find a path P in a graph for which the number of vertices in the largest component of G-P is minimized. The relationships among these concepts are studied. Most of the results presented are for trees, and, in particular, linear algorithms for finding paths in trees of minimum eccentricity and of minimum branch weight are presented. These problems arise in determining a “most accessible” linear route in a network according to several plausible criteria.

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