  For many networks, it is useful to think of their nodes as being embedded in
a latent space, and such embeddings can affect the probabilities for nodes to
be adjacent to each other. In this paper, we extend existing models of
synthetic networks to spatial network models by first embedding nodes in
Euclidean space and then modifying the models so that progressively longer
edges occur with progressively smaller probabilities. We start by extending a
geographical fitness model by employing Gaussian-distributed fitnesses, and we
then develop spatial versions of preferential attachment and configuration
models. We define a notion of "spatial strength centrality" to help
characterize how strongly a spatial embedding affects network structure, and we
examine spatial strength centrality on a variety of real and synthetic
networks.
