Motivated by recent developments in physical-layer security and stochastic geometry, we aim to characterize the fundamental limits of secure communication in wireless networks. Based on a general model in which legitimate nodes and potential eavesdroppers are randomly scattered in space, we define the secure communication graph (s-graph) from the point of view of information-theoretic security. For the Poisson s-graph, we provide conclusive results for: (a) the in-degree and out-degree of a node; (b) the isolation probability; and (c) the secrecy capacity between a node and each of its neighbours. Our analysis reveals the innate connections between information-theoretic security and the spatial densities of legitimate and eavesdropper nodes.