This paper reviews, classifies and compares recent models for social networksthat have mainly been published within the physics-oriented complex networksliterature. The models fall into two categories: those in which the addition ofnew links is dependent on the (typically local) network structure (networkevolution models, NEMs), and those in which links are generated based only onnodal attributes (nodal attribute models, NAMs). An exponential random graphmodel (ERGM) with structural dependencies is included for comparison. We fitmodels from each of these categories to two empirical acquaintance networkswith respect to basic network properties. We compare higher order structures inthe resulting networks with those in the data, with the aim of determiningwhich models produce the most realistic network structure with respect todegree distributions, assortativity, clustering spectra, geodesic pathdistributions, and community structure (subgroups with dense internalconnections). We find that the nodal attribute models successfully produceassortative networks and very clear community structure. However, they generateunrealistic clustering spectra and peaked degree distributions that do notmatch empirical data on large social networks. On the other hand, many of thenetwork evolution models produce degree distributions and clustering spectrathat agree more closely with data. They also generate assortative networks andcommunity structure, although often not to the same extent as in the data. TheERG model turns out to produce the weakest community structure.
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