The existence of an actor as a set of asymmetric relations to and from every actor in a network of relations is specified as the position of the actor in the network. Conditions of strong versus weak structural equivalence of actor positions in a network are defined. Network structure is characterized in terms of structurally nonequivalent, jointly occupied, network positions located in the observed network. The social distances of actors from network positions are specified as unobserved variables in structural equation models in order to extend the analysis of networks into the etiology and consequences of network structure.