On the Conditional Entropy of Wireless Networks

The characterization of topological uncertainty in wireless networks using the formalism of graph entropy has received interest in the spatial networks community. In this paper, we develop lower bounds on the entropy of a wireless network by conditioning on potential network observables. Two approaches are considered: 1) conditioning on subgraphs, and 2) conditioning on node positions. The first approach is shown to yield a relatively tight bound on the network entropy. The second yields a loose bound, in general, but it provides insight into the dependence between node positions (modelled using a homogeneous binomial point process in this work) and the network topology.