# MoN17: Seventeenth Mathematics of Networks meeting

## Exploiting symmetries in network analysis – Ruben Sanchez Garcia (Southampton)

Virtually all network analyses involve structural measures or metrics between pairs of vertices, or of the vertices themselves. The large amount of redundancy present in real-world networks is inherited by such measures, and this has practical consequences which have not yet been explored in full generality, nor systematically exploited by network practitioners. Here we develop a complete framework to study and quantify the effect of redundancy on arbitrary network measures, and explain how to exploit redundancy in practice, achieving, for instance, remarkable lossless compression and computational reduction ratios in several real-world networks against some popular measures, and predicting and explaining most of the discrete part of the spectrum of a network measure such as the graph Laplacian. We show that computing network symmetries is very efficient in practice, testing real-world examples up to several million nodes.

Bio: I am a Lecturer in Mathematical Sciences at the University of Southampton. I did my undergraduate degree at the Universidad de MÃ¡laga (Spain), then a PhD at the University of Southampton, and I held postdoctoral positions at the University of Sheffield, DÃ¼sseldorf and Southampton.

I have a pure mathematics background in Algebraic Topology, although I am currently working in the interface between pure and applied mathematics within complexity theory, particularly mathematical aspects of complex networks, and topological data analysis.

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