This repository contains my mini-projct carried out for the Networks course as part of the MSc Mathematical Sciences at the University of Oxford.
Several works in recent years have investigated the possibility to characterise the geometry of real-world networks. Important questions include the non-Euclidean geometry of network latent spaces, but also measures for the discrete curvature of networks, including the Ollivier-Ricci and Forman-Ricci curvatures. The objective of this mini-project was to write a report on a specific subtopic within the general heading of network geometry. The report includes original numerical simulations and a personal description of the mathematical methods. (unsupervised) The project was compltetely independent and also had a role-play element to it. As such, the report is in the format and style of an article for the journal Proceedings of the National Academy of Sciences (PNAS) but note that the report was not submitted to PNAS.
Ollivier-Ricci and Forman-Ricci curvatures are two well-studied approaches for discretising Ricci curvature for nodes and links of graphs. Recently, a novel approach based on the concept of effective resistance has been introduced, namely resistance curvature. This report introduces various notions of discrete Ricci curvature for undirected, weighted graphs and compares those that are well-established with the new resistance curvatures.
The full report can be found here and Supplementary Information can also be found here.
