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. 
Melanie Weber, Emil Saucan and J\"urgen Jost
cs.DM cs.SI math.CO