On centrality functions of a graph
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.
- Christofides, N.: "Graph theory, an algorithmic approach", Academic Press, London, 1975Google Scholar
- Sabidussi, G.: "The centrality index of a graph", Theory of graphs, International Symposium, Rome, pp. 369–372, 1966Google Scholar
- 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
- 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
- Kajitani, Y.: "Centrality of vertices in a graph", Proc. 1979 International Colloq. on Circuits & Systems, Taipei, July 1979Google Scholar
- 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