Applications of Graph Theory to Group Structure

Applications of Graph Theory to Group Structure

Applications of Graph Theory to Group Structure

Applications of Graph Theory to Group Structure


It is easily granted that a science that has attained its maturity must become mathematical and must therefore make use of numbers.

This therefore seems to us to be contestable. Numbers — or more exactly numerical sets — are members of the family of mathematical structures. To translate a problem into mathematical terms consists of defining at least a partial isomorphism between this problem and an adequate mathematical structure. This structure may or may not be numerical, the essential aspect being that it is adequate: the isomorphism must be demonstrable.

The numerical structures are particularly rich — their properties are numerous and highly complex — but it is rare that a behavioral fact can be shown to have such properties (and even more rare that the question is raised); therefore a numerical model is rarely legitimate!

We shall therefore mathematize many problems of the behavioral sciences through the use of poorer structures, having fewer properties, and having properties that are simpler — that is, that can be more easily identified in reality.

The theory of graphs, which will be shown to be the mathematical theory of arbitrary relations, provides us with some of those structures that are poor in properties that cannot be observed in behavior, but that are rich in potentialities of application to the behavioral sciences.

It is often thought that the theory of graphs can be useful only for static descriptions; this is not the case, as we shall try to show in Chapter 3. But it must be admitted that all the potentialities of the theory of graphs as . . .

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