Graph Theory and Algorithms pp 45-52 | Cite as

# On centrality functions of a graph

Conference paper

First Online:

## Abstract

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.

## Keywords

Directed Graph Centrality Function Stability Theorem Opposite Edge Tokyo Institute
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Download
to read the full conference paper text

## References

- [1]Christofides, N.: "Graph theory, an algorithmic approach", Academic Press, London, 1975Google Scholar
- [2]Sabidussi, G.: "The centrality index of a graph", Theory of graphs, International Symposium, Rome, pp. 369–372, 1966Google Scholar
- [3]Kajitani, Y. and Maruyama, T.: "Functional extention of centrality in a graph", Trans. IECE Japan, vol. 59, pp. 531–538, July 1976 (in Japanese)Google Scholar
- [4]Kishi, G. and Takeuchi, M.: "On centrality functions of a non-directed graph", Proc. of the 6th Colloq. on Microwave Comm., Budapest, Aug. 1978Google Scholar
- [5]Kajitani, Y.: "Centrality of vertices in a graph", Proc. 1979 International Colloq. on Circuits & Systems, Taipei, July 1979Google Scholar
- [6]Kishi, G. and Takeuchi, M.: "Centrality functions of directed graphs", Tech. Rep. CST 77–106, Technical Group on Circuit and System Theory, IECE Japan, Dec. 1977 (in Japanese)Google Scholar

## Copyright information

© Springer-Verlag Berlin Heidelberg 1981