Talk Sanjukta Krishnagopal
Mar 14, 2022 -
Sanjukta Krishnagopal from the University College London will present her work on higher order network representations.
- Title: Investigating the community structure of complex interaction data through a simplicial complex formulation.
- Date: Wednesday, 16 March 2022 at 11:00 - 12:00
- Room: HG E23
Community detection in complex networks has been very successful in understanding several systems where interactions are inherent. The conventional Laplacian encodes many dynamical properties of a network, including community structure and flow of information along the network. While networks are a useful tool to represent data in the graphical domain, most systems naturally evolve to contain simultaneous interactions between more than two entities, represented as simplices - triangles, tetrahedra etc. Here I present the first work on community detection in these ‘higher-order networks’ called simplicial complexes that are more appropriate to model several types of systems. I reveal the relationship between a higher order equivalent of the Laplacian (Hodge Laplacian) and simplicial communities, demonstrating our results on both synthetic networks, as well as social and language networks. In the absence of many datasets with higher-order interactions pre-coded, I present a method to infer higher-order simplicial complexes from the network backbone, a question of some importance. Lastly, I present recent work on how simplicial complexes can be used to model social interactions in the context of extreme mountaineering, and study how expedition styles (from co-operative to competitive), informed by the topological structure of climber-relationships, affect success at high peaks.