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In this paper we present a novel mathematical approach to evaluate the degree of connectivity of a multi- sink wireless sensor network, where sink and sensor nodes are uniformly distributed over a given region. We consider both unbounded and bounded domains, specifically squares, and the impact of border effects is also shown. Random fluctuations as well as a distance-dependent deterministic path-loss are accounted for in our radio channel model. In particular, we deal with randomly shaped wireless footprints, rather than with the less realistic (yet widely adopted) disk model, which is a special case of our channel model. Nodes are organized in a tree-based topology with trees rooted at the sinks (multi-hop communications). The approach allows the computation of the probability that a randomly chosen sensor is not isolated, from which the probability that a certain amount of nodes are connected can be …