A random geometric graph built on a time-varying Riemannian manifold

• DOI: 10.1016/j.physa.2015.05.076
• Publication Date: 2015-05-19T18:02:07Z
• Authors: Zheng Xie; Jiang Zhu; Dexing Kong; Jianping Li
• Keywords: Geometric flow; Random geometric graph; Geometric networks; Geometric graph theory; Manifold (fluid mechanics); Riemannian manifold; Geometric analysis; Statistical manifold

Abstract The theory of random geometric graph enables the study of complex networks through geometry. To analyze evolutionary networks, time-varying geometries are needed. Solutions of the generalized hyperbolic geometric flow are such geometries. Here we propose a scale-free network model, which is a random geometric graph on a two dimensional disc. The metric of the disc is a Ricci flat solution of the flow. The model is used to physically simulate the growth and aggregation of a type of cancer cell.