WebNov 16, 2024 · We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. WebOur model of emergent geometry is based on a growing simplicial complex. Metric spaces satisfy the triangular inequality, therefore a network with non-trivial geometry should include a high clustering coefficient and high density of triangles, ensured by building the …

2001 BULLETIN OF MATHEMATICAL BIOLOGY complex systems EMERGENT …

WebDec 10, 2014 · Abstract: Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly … WebNevertheless we still miss a model in which networks develop an emergent complex geometry. Here we show that a single two parameter network model, the growing geometrical network, can generate complex network geometries with non-trivial dis-tribution of curvatures, combining exponential growth and small-world properties boycott arms shipley

A simple differential geometry for complex networks

WebIntroduction. Network Theory has provided a large evidence that network topology affects the dynamics and function of complex networks 1 – 7.Recently, growing attention has been devoted to analyze networks not only from the topological viewpoint but, also, from a geometrical perspective 8 – 11.Characterizing the geometry of complex networks is … WebEmergent Hyperbolic Network Geometry Ginestra Bianconi 1 & Christoph Rahmede 2 A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. boycott aquaman