Biologists seek an understanding of the processes underlying spatial biodiversity patterns. Neutral theory links those patterns to dispersal, speciation and community drift. Here, we advance the spatially explicit neutral model by representing the metacommunity as a network of smaller communities. Analytic theory is presented for a set of equilibrium diversity patterns in networks of communities, facilitating the exploration of parameter space not accessible by simulation. We use this theory to evaluate how the basic properties of a metacommunity - connectivity, size, and speciation rate - determine overall metacommunity gamma-diversity, and how that is partitioned into alpha- and beta-components. We find spatial structure can increase gamma-diversity relative to a well-mixed model, even when theta is held constant. The magnitude of deviations from the well-mixed model and the partitioning into alpha- and beta-diversity is related to the ratio of migration and speciation rates. gamma-diversity scales linearly with metacommunity size even as alpha- and beta-diversity scale nonlinearly with size.