| This dissertation focuses on the formal theoretical and methodological treatment of large, spatially embedded interpersonal networks, combining empirical findings regarding interaction in space with a stochastic modeling perspective. A simple framework is developed for the modeling of such networks, based on the relationship between socio-physical distance and tie probability. An examination of three data sets suggests that---in the case of physical distance---this relationship takes the form of a power law, whose parameters vary with relational content. It is shown that the inferred distance/tie probability relationship is strong enough to account for the overwhelming majority of uncertainty in network structure at large (e.g. 100 x 100km) spatial scales, and it is argued that this result is robust to the specific form of the relationship in question. It is also demonstrated that the distance/tie probability relationship leads to a special form of stochastic equivalence, which in turn motivates the treatment of urban agglomerations as unitary entities for certain applications. Several families of descriptive indices are introduced for the description of spatially-embedded networks, and their behavior is discussed. Finally, extrapolative simulations are employed to predict spatial macrostructure across large geographical regions, using a combination of demographic data and fitted tie probability models. |
