Topological implications of negative curvature for biological and social networks

Abstract

Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parameterized finite networks, and show that a variety of biological and social networks are hyperbolic. This hyperbolicity property has strong implications on the higher-order connectivity and other topological properties of these networks. Specifically, we derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks. We describe two implications of these bounds to cross-talk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.

arXiv commentPhysical Review E, 2014

References in corpus (12)

• Statistical mechanics of complex networks
• Community structure in social and biological networks
• Cooperative Game Theory Approaches for Network Partitioning
• The large-scale organization of metabolic networks
• Dynamic reconfiguration of human brain networks during learning
• Community Structure in Jazz
• Detecting rich-club ordering in complex networks
• Sustaining the Internet with Hyperbolic Mapping
• Predicting essential components of signal transduction networks: a dynamic model of guard cell abscisic acid signaling
• The Large Scale Curvature of Networks
• Euclidean versus hyperbolic congestion in idealized versus experimental networks
• A New Computationally Efficient Measure of Topological Redundancy of Biological and Social Networks

Cited by in corpus (16)

• Network Geometry
• Network geometry with flavor: from complexity to quantum geometry
• Interdisciplinary and physics challenges of Network Theory
• Weighted Growing Simplicial Complexes
• Complex Quantum Network Geometries: Evolution and Phase Transitions
• Topological Percolation on Hyperbolic Simplicial Complexes
• Hyperbolicity Measures "Democracy" in Real-World Networks
• Self-Organised Criticality and Emergent Hyperbolic Networks -- Blueprint for Complexity in Social Dynamics
• On analyzing and evaluating privacy measures for social networks under active attack
• Effect of Gromov-hyperbolicity Parameter on Cuts and Expansions in Graphs and Some Algorithmic Implications
• Link prediction for egocentrically sampled networks
• Local topological moves determine global diffusion properties of hyperbolic higher-order networks
• Finding Influential Cores via Normalized Ricci Flows in Directed and Undirected Hypergraphs with Applications
• Lorentzian Graph Convolutional Networks
• Negatively Curved Graphs
• Curvature of an Arbitrary Surface for Discrete Gravity and for $d=2$ Pure Simplicial Complexes