Network functions in the presence of symmetry

Ruben Sanchez-Garcia, University of Southampton. Part of the Leeds applied nonlinear dynamics seminars series.

Network models inherit all the redundancies of the system they represent, and they manifest themselves as symmetries of the underlying graph. The presence of such symmetries, a remarkable feature of real-world networks, have profound consequences on network structure and eigenvalues, and, crucially, symmetries are inherited by any function, or measurement, on the network. In this talk, I will explain the theoretical framework to study network symmetry in the context of arbitrary network functions, and the practical consequences of redundancies for compression, computational reduction, and spectral decomposition.

The talk will start with an overview of previous and current work in applied graph theory and topology, including spectral clustering for power transmission networks, and the discrete Laplacian applied to ranking in horse racing.

Ruben Sanchez-Garcia, University of Southampton