Algebraic Topology in Networks

In determining whether a network has full coverage or not, say in a cellular phone network, one obtains an answer by collecting geographical data and making calculations.  This usually implies that one knows the precise locations of cell phone towers.  However, we explore a way in which abstract algebra and topology, both pure mathematical theories, provide an answer to the coverage problem where exact locations are not necessary.  Furthermore, we discuss how we would like to expand this idea in the situation where cell phone towers are replaced by general sensors, and where the network itself is a dynamical object.  The purpose is to demonstrate that an abstract theory in mathematics can be used to solve an applied problem.