Graph Theoretic Methods in the Management Sciences

The purpose of this paper is to illustrate the potential utility of graph theoretical methods for the management sciences. In a series of joint papers (16, 17, 18,19, 20) with I. C. Ross, we have combined a graph theoretical approach with matrix theory and set theory to handle problems concerning redundancies, liaison persons, cliques, and strengthening and weakening members of a group. The correspondence between these organizational concepts and ideas from graph theory (to be explained below) is as follows. A redundancy is analogous to a directed path which passes through the same point more than once. A liaison person in an organization has the role of a cut point of a connected graph. A clique is taken as a maximal complete subgraph. A strengthening member of a group is one whose presence causes the graph of a group to be more highly connected that the graph obtained when he is absent.