Measuring Entanglement in Physical Networks

The links of a physical network cannot cross, which often forces the network layout into nonoptimal entangled states. Here we define a network fabric as a two-dimensional projection of a network and propose the average crossing number as a measure of network entanglement. We analytically derive the dependence of the average crossing number on network density, average link length, degree heterogeneity, and community structure and show that the predictions accurately estimate the entanglement of both network models and of real physical networks.Received 8 March 2024Accepted 27 June 2024DOI:https://doi.org/10.1103/PhysRevLett.133.077401© 2024 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCommunity structureDegree distributionsNetwork structureTechniquesNetworks Analysis ToolsNetworks