On centrality functions of a graph

  • G. Kishi
Conference paper

DOI: 10.1007/3-540-10704-5_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 108)
Cite this paper as:
Kishi G. (1981) On centrality functions of a graph. In: Saito N., Nishizeki T. (eds) Graph Theory and Algorithms. Lecture Notes in Computer Science, vol 108. Springer, Berlin, Heidelberg


For a connected nondirected graph, a centrality function is a real valued function of the vertices defined as a linear combination of the numbers of the vertices classified according to the distance from a given vertex. Some fundamental properties of the centrality functions and the set of central vertices are summarized. Inserting an edge between a center and a vertex, the stability of the set of central vertices are investigated.

For a weakly connected directed graph, we can prove similar theorems with respect to a generalized centrality function based on a new definition of the modified distance from a vertex to another vertex.

Copyright information

© springer-Verlag 1981

Authors and Affiliations

  • G. Kishi
    • 1
  1. 1.Graduate School of Coordinated Science Tokyo Institute of TechnologyMidori-ku, YokohamaJapan

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