With a grant from the German-Israeli Foundation for Scientific Research and Development (GIF) our director Jürgen Jost and Emil Saucan from the Braude College Israel will continue their successful scientific collaboration for the next three years. Their research focus lies on discrete curvatures for networks, their comparison and applications. Congratulations!
Their current research project is devoted to the extension and further development of their geometric approach to the study of complex networks. Jost and Saucan focused on the adaptation of Forman's Ricci curvature to the setting of networks and their generalizations. In particular, they wish to explore, both theoretically and experimentally the various types of suitable Ricci flows, specifically their role in understanding and prediction of long-term development of large scale, real life networks.
They also would like to explore the connection between this type of curvature and its higher dimensional counterparts and their connection to the respective Bochner Laplacians and exploit their joint properties for topological data analysis purposes.
Furthermore, they propose a different approach to the definition of curvature measures for networks, based on their embedding in certain convex polyhedra and comparison with various notions of curvature for simplicial and more general polyhedral manifolds. Other notions of curvature for networks, in particular metric ones are also proposed.
Curvature-colored network plot of a Google web graph.
The roughly 1000 nodes represent webpages, while the edges connecting them denote hyperlinks. The darker their color, the higher the absolute value of curvature. The higher curvature of a node, the larger the black disk representing it. This is a directed (not-symmetric) graph, thus a webpage might have many different connections to others.
Characterizing complex networks with Forman-Ricci curvature and associated geometric flows
Melanie Weber, Emil Saucan, Jürgen Jost
Journal of Complex Networks, Volume 5, Issue 4, August 2017, Pages 527–550