Centrality functions of a network with capacities on vertices and edges

When using a graph to represent a system with a network architecture, such as a communications network or a transport network, debating the degree of centrality of vertices in the graph and finding locations of the vertices w ith the greatest amount of centrality is one topic of interest in graph and network theory. With respect to this problem, various different methods ha ve been considered for representing, the centrality of vertices in a graph or a network. In general, this is referred to as a "centrality function." M ost centrality functions use either the distance between two vertices or th e maximum flow between two vertices. Centrality functions that use the maxi mum flow value are obtained with respect to a network with capacities in ei ther the: vertices or the edges. No centrality function has been defined fo r a network with capacities in both the vertices and the edges. In this pap er the authors consider a centrality function for a network with capacities in the vertices and edges. This centrality function is defined using not o nly the capacity of the edges but also the maximum flow between two vertice s in the network obtained based on the relay capability of the vertices, an d is thus considered significant. (C) 2001 Scripta Technica.