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

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.

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