Abstract
Standard measures of the centrality, or suitability as a site for a facility, of a vertex in a network include the eccentricity, branch weight, and distance sum. The nature of the facility to be constructed (such as a pipeline) could necessitate selecting a structure (such as a path) rather than just a point at which to locate the facility. Similarly, the facility may be required to "service" structures or areas within the network, and not just points. The same three measures of centrality can be applied to structures within the network, and it is proposed that four classes of locational problems should be considered : vertex-serves-vertex, vertex-serves-structure, structure-serves-vertex and, most generally, structure-serves-structure.
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© 1984 Springer-Verlag
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Slater, P.J. (1984). Some definitions of central structures. In: Koh, K.M., Yap, H.P. (eds) Graph Theory Singapore 1983. Lecture Notes in Mathematics, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073115
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DOI: https://doi.org/10.1007/BFb0073115
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