Spheres, Cubes and Boxes: Graph Dimensionality and Network Structure *

Dimensional ideas are common in every branch of science. Social network analysis is no exception. Almost every study of social networks involves discussion of the parameters, factors or dimensions underlying and embodied in the pattern of relations that is being examined. Different words are used, but the idea is the same; we would like to be able to reduce the enormous number of structural characteristics of networks to a relatively small set that are somehow basic or fundamental. One way to approach this problem is by examining the dimensionality of a network of interest. In so doing, one is asking about the structural complexity of the object being studied. Is this, one asks, a simple pattern that varies, say, with respect to a single characteristic. Or is it so complex that it requires taking five or ten or twenty different features into account? These are the sorts of questions that lead to a concern with dimensionality in social networks research. And these are the sorts of ques-