Graph Theory and Social Networks: A Technical Comment on Connectedness and Connectivity

Abstract

Concepts taken from graph theory and other branches of topology have been used by many sociologists and social psychologists, in particular Kurt Lewin and J. L. Moreno. Similar ideas have been used to construct statistical models of nervous systems, and these have been applied by J. S. Coleman and others to the spread of information and other social phenomena. The study of social networks by anthropologists has been based, knowingly or unknowingly, on the basic notions of graph theory, as has the identification and analysis of social cliques. There is little consensus among mathematicians about terminology, and social scientists have drawn fortuitously on various mathematical vocabularies as well as inventing their own technical terms. Applied to social networks, the words `connectedness' and `connectivity' may refer to properties of the distance between persons, the number of paths between them, whether there is a path at all, or the proportion of possible paths actually in existence. These different usages are contrasted by restating them all in the terminology set out in Structural models (1965) by Harary, Norman and Cartwright.