Graphs resulting from human behavior (the web graph, friendship graphs, etc.) have hitherto been viewed as a monolithic class of graphs with similar characteristics; for instance, their degree distributions are markedly heavy-tailed. In this paper we take our understanding of behavioral graphs a step further by showing that an intriguing empirical property of web graphs --- their compressibility--- cannot be exhibited by well-known graph models for the web and for social networks. We then develop amore nuanced model for web graphs and show that it does exhibit compressibility, in addition to previously modeled web graph properties.