Before revision: This paper considers a general form of network dependence where dependence between two sets of random variables becomes weaker as their distance in a networkgets longer. We show that such network dependence cannot be embedded as a random field on a lattice in a Euclidean space with a fixed dimension when the maximum clique increases in size as the network grows. This paper applies Doukhan and Louhichi (1999) 's weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables.
After revision: This paper is concerned with cross-sectional dependence arising because observations are interconnected through an observed network. Following Doukhan and Louhichi (1999) 's weak dependence notion to network dependence by measuring dependence strength by the covariance between nonlinearly transformed random variables.