The starting point of this paper is a flexible framework for the analysis of social network data using exponential random graph models (ERGMs) based on a two-dimensional hierarchy of potential dependence structures for network tie variables (Pattison, Robins, Snijders & Wang, 2011). We review the ERGM form implied by each dependence structure and describe how the hierarchy of dependence structures, in conjunction with existing approaches to the efficient parameterisation of related network effects, leads to models that reflect network processes of cohesion, closure, brokerage and/or connectivity over short or longer network distances. We demonstrate the variety of network structures to which these model forms give rise and illustrate their application to data based on a complete census of network ties as well as various sampling schemes for network data, including snowball or contact-tracing approaches.