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By Claude Flament

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Extra info for Applications of graph theory to group structure (Prentice-Hall series in mathematical analysis of social behavior)

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On the national and international levels, we hardly need mention the importance of systems of telecommunication. The set of physical conditions allowing communication within a group will be referred to as a communication network. It is but a generalization of the usual expression: telephone network, postal network, road network, etc. The development of a network of communication in a group often is not based on valid scientific criteria. Nevertheless, the choice of which particular network is established matters to the group, since its life can be greatly affected thereby.

It is but a generalization of the usual expression: telephone network, postal network, road network, etc. The development of a network of communication in a group often is not based on valid scientific criteria. Nevertheless, the choice of which particular network is established matters to the group, since its life can be greatly affected thereby. Therefore, the psycho-sociological problem raised is the following: 47 48 COMMUNICATION NETWORKS in what way does the life of the group depend on the available communication network?

Paths of a Graph We call a path of a graph G = (X; V) a completely ordered subset V' of V such that the kth arc of V' ends at the point of X from which the (k + 1)th arc is coming out; if x is the source of the first arc of V' and y, the ending of the last arc of V', the path may be denoted y(xy). Example. In the graph of Fig. 15, let V' = {(j, e), (e, d), (d, a)}; we get a path y(ja). da). If one wants to specify all the steps of the path, one writes y(jeda). If the graph represents a road network with its one-way streets, we realize that a path represents in fact a possible route.

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Applications of graph theory to group structure (Prentice-Hall series in mathematical analysis of social behavior) by Claude Flament


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