# Network connectivity in complex geometries

**Speaker:** Carl Dettmann, School of Mathematics, University of Bristol

**Title:** Network connectivity in complex geometries

**Abstract:** We consider connectivity of spatial networks using a general model called a soft random geometric graph. Nodes are located randomly, and links formed with a probability depending on the mutual distance. This model has a natural application to wireless mesh networks, for which the link probability function can be derived from assumptions about the channel characteristics. We derive a formula for the connection probability applicable to uniform node distributions in convex domains with arbitrary piecewise smooth boundaries and arbitrary link probability function. We then consider complex boundaries, for which adding nodes can paradoxically reduce connectivity. Finally, we consider alternative node distributions, and show that uniformity of the distribution is usually more important than complexity of the geometry.