Riemannian-geometric entropy for measuring network complexity

Abstract

A central issue of the science of complex systems is the quantitative characterization of complexity. In the present work we address this issue by resorting to information geometry. Actually we propose a constructive way to associate to a - in principle any - network a differentiable object (a Riemannian manifold) whose volume is used to define an entropy. The effectiveness of the latter to measure networks complexity is successfully proved through its capability of detecting a classical phase transition occurring in both random graphs and scale--free networks, as well as of characterizing small Exponential random graphs, Configuration Models and real networks.

15 pages, 3 figures

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• Modularity and community structure in networks
• Critical phenomena in complex networks
• The entropy of randomized network ensembles
• The Shannon and the Von Neumann entropy of random networks with heterogeneous expected degree
• Asymptotic entropy and green speed for random walks on countable groups
• The diminishing role of hubs in dynamical processes on complex networks
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Cited by in corpus (8)

• Network Geometry
• Information geometric methods for complexity
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Microcanonical entropy for classical systems
• Towards an Information Geometric characterization/classification of Complex Systems. I. Use of Generalized Entropies
• Entanglement estimation in non-optimal qubit states
• Entropic Dynamics of Networks
• Catching homologies by geometric entropy