  We provide a framework for modeling social network formation through
conditional multinomial logit models from discrete choice and random utility
theory, in which each new edge is viewed as a "choice" made by a node to
connect to another node, based on (generic) features of the other nodes
available to make a connection. This perspective on network formation unifies
existing models such as preferential attachment, triadic closure, and node
fitness, which are all special cases, and thereby provides a flexible means for
conceptualizing, estimating, and comparing models. The lens of discrete choice
theory also provides several new tools for analyzing social network formation;
for example, the significance of node features can be evaluated in a
statistically rigorous manner, and mixtures of existing models can be estimated
by adapting known expectation-maximization algorithms. We demonstrate the
flexibility of our framework through examples that analyze a number of
synthetic and real-world datasets. For example, we provide rigorous methods for
estimating preferential attachment models and show how to separate the effects
of preferential attachment and triadic closure. Non-parametric estimates of the
importance of degree show a highly linear trend, and we expose the importance
of looking carefully at nodes with degree zero. Examining the formation of a
large citation graph, we find evidence for an increased role of degree when
accounting for age.
