# MoN17: Seventeenth Mathematics of Networks meeting

## Network connectivity in complex geometries – Carl Dettmann (Bristol)

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. Then we consider alternative node distributions, and show that uniformity of the distribution is usually more important than complexity of the geometry. Very non-uniform distributions are difficult to connect with a high probability unless the typical connection range, and hence power requirements, are increased.

Bio: Carl Dettmann obtained a BSc(Hons) and PhD in physics at the University of Melbourne, Australia in 1991 and 1995 respectively. After postdoctoral research at New South Wales, Northwestern, Copenhagen and Rockefeller Universities he moved to the University of Bristol where he is now Professor of Applied Mathematics. He has over 120 papers in statistical physics, dynamical systems and wireless networks. With Justin Coon he leads the £1.2M EPSRC project Spatially Embedded Networks.
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Keith Briggs
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Richard G. Clegg (richard@richardclegg.org)