The interaction of size and density with graph-level indices

Ž . The size and density of graphs interact powerfully and subtly with other graph-level indices GLIs , thereby complicating their interpretation. Here we examine these interactions by plotting changes in the distributions of several popular graph measures across graphs of varying sizes and densities. We provide a generalized framework for hypothesis testing as a means of controlling for size and density effects, and apply this method to several well-known sets of social network data; implications of our findings for methodology and substantive theory are discussed. q 1999 Elsevier Science B.V. All rights reserved. Ž . JEL classification: C150 Statistical simulation and Monte Carlo methods