13 - Random Graph Models

Summary

Introduction

The main purpose of social network analysis is detecting and interpreting patterns of social ties among actors (Chapter 1). A pattern of social ties is meaningful if it expresses choices by social actors or the impact of the social system on actors’ behavior and attitudes. Until now, we have implicitly assumed that the observed network expresses choices or social constraint, although we have pointed out that our behavioral interpretations should be checked by comparing them with other indicators – for example, see the discussion on structural and social prestige in Chapter 9.

In the current chapter, we accept the idea that at least part of the structure of the observed network is random. As a consequence, we should not assume that every pattern found in a network is meaningful. Statistical inference should tell us whether a network characteristic is random. We do not use statistical inference in the classic sense, assuming that the observed network is a random sample from a larger network (design-based inference). For some basic network properties, statistical inference based on a random sample is possible, but that is not what we pursue here. Instead, we present statistical network models that tell us which network characteristics to expect if the lines are assigned to pairs of vertices according to a random process (model-based inference). This approach assumes that network structure could have been different; for example, the line between actors v and u (Figure 128, network C) could have been replaced by a line between v and w (Figure 128, network D), but not every network structure is necessarily equally probable.