Predictability of Large-scale Spatially Embedded Networks

It is shown that upper bounds on the marginal edge probabilities for farflung dyads can be used to place a lower bound on the predictive power of distance, and one such bound is applied and suggests that only modest constraints are required for distance effects to dominate at large physical scales.

Abstract

Although it is well-known that there is a relationship between socio-physical dis- tance and edge probability in interpersonal networks, the predictive power of such distances for total network structure has not been established. Here, it is shown that upper bounds on the marginal edge probabilities for farflung dyads can be used to place a lower bound on the predictive power of distance, and one such bound is de- rived. Application of this bound to the special case of uniformly placed vertices on the plane suggests that only modest constraints are required for distance effects to dominate at large physical scales.