Characterizing complex networks with Forman-Ricci curvature and associated geometric flows

We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mathematical motivation, we apply the proposed network-analytic methods to static and dynamic complex networks and compare the results with established node-based characteristics. Our work suggests a number of applications for data mining, including denoising and clustering of experimental data, as well as extrapolation of network evolution. Complex networks, FormanRicci-curvature, Ricci-flow, Laplacian flow, data mining 2000 Math Subject Classification: 05C82, 05C75, 05C21, 05C10 Contact: [email protected], [email protected], [email protected]