**Graph theory and Physics, 30th May 2018, Imperial College London**

*Report by Matt Garrod*

The Institute of Physics’ Nonlinear and Complex Physics Group held their Spring meeting on Wednesday the 30th of May. The event which was entitled “Graph Theory and Physics” and was held at Imperial College London. The event attracted approximately 30 attendees from a wide variety of disciplines, both from Imperial College and other institutions around the country.

Many physicists are active researchers in the field of complex networks, which often makes use of tools from statistical physics and graph theory to study networks which crop up in fields of research such as biology, economics and the social sciences. However, as it turns out, there are a plethora of different applications of graph theory even within physics itself. The aim of the event was to explore these connections and provide an opportunity for those working in physics to be introduced to mathematical ideas from graph theory and vice versa.

The morning mostly focused on applications of graph theory to quantum physics. The first talk from Svenn Gnutzmann of University of Nottingham discussed the applications of graph theory in the study of quantum chaos while UCL’s Professor Simone Severini discussed the application of graphs to quantum information theory. These ideas were explored further later in the day by Loughborough University’s Brian Winn.

The following two talks showcased how the interdisciplinary nature of graph theory make it a rich source for collaboration. Dhruv Saxena and Alexis Arnaudon are both postdoctoral researchers at Imperial College from the departments of physics and mathematics respectively. Dhruv is physicist based in the Complex Nanophotonics group within Imperial who’s work concerns so called “random networks of optical lasers”. Dhruv’s talk introduced the physics of the problem and the experimental setup of photonic lasers. Following this, Alexis introduced his own mathematical of the model of the system created in order to gain some insight into how such systems behave and how they might be controlled.

Many of the talks focused on using graph theory to study physics at small scales. The next talk given by Stav Zalel, a PhD student in theoretical physics at Imperial College provided a contrast to this. Stav spoke about her work in studying “causal sets” which are one candidate approach to quantum gravity. This research is relevant for modelling and understanding the large scale structure of the universe. Following this, David Reutter, a PhD student at the University of Oxford, provided a talk showcasing his work which lies at the intersection of quantum information, compact quantum groups and category theory.

The rest of the Afternoon saw several talks concerning some of the applications of graph theory and network science to fields other than Physics. Oliver Smith spoke about the analysis of flows in complex networks with respect to a metric known as the Price of Anarchy. While the final student speaker of the day, Imperial College’s Ronan Macadam described the analysis of transport of plastic through the “connectivity network” of different regions in the ocean using a Markov-Chain based model.

The final talk of the day was given by Professor Ernesto Estrada, a prominent researcher in the field of network science, who has published numerous papers as well as two text books on the subject. In his talk he introduced the idea of communicability on networks. Researchers commonly use the average shortest path between nodes in a graph to measure how well connected the system is. Communicability provides an alternative measure which is motivated by how information or messages are actually known to pass through a graph, which is not necessarily by using the shortest path or most efficient route. Following the final talk was a drinks reception which provided an opportunity for researchers to network and discuss the topic further.