This paper clarifies the structural and behavioral characteristics of minimum distance networks of diameter 2 and the relationship between the formation of minimum distance networks and the small-world phenomenon. These networks are evaluated in terms of efficiency of indirect contact/communication, parsimony in the use of edges, nonseparability, and expected inefficiency under the random elimination of a single node. Related existing graph-theoretic theorems are reviewed and are integrated into a description of these networks. In addition, a rational choice theory of ego-centric network ties is introduced to evaluate the relevance of minimum distance networks for the small-world phenomenon. In particular, Nash equilibria derived from utility models of ego-centric network ties for rational actors are described.