Abstract
In 1956, French [3] proposed the use of the theory of finite directed graphs in studying the structure of social groups, in dealing with convergence of opinions, given a structure of influence among the elements of those social groups. Three years later Harary [4] extended the problem and presented results for the case in which there is or is not influence of one individual of the group on the others. In this paper we present a rigorous mathematical formulation of the problem and extend the results to the case in which we have gradation of influence between individuals. This corresponds, in our case, to having the elements of the matrix R lying in the interval $( {0,1} ]$, while Harary had only zeros and ones in his case. The situation of no influence of one individual on another corresponds to a zero in the adjacency matrix.
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