Complex Networks as Hypergraphs

Abstract

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited information about the structure of the system. We propose to use hypergraphs to represent these systems by introducing the concept of the complex hyper-network. We define several structural measures for complex hyper-networks. These measures characterize hyper-network structures on the basis of node participation in different hyper-edges (groups) and sub-hypergraphs. We also define two clustering coefficients, one characterizing the transitivity in the hyper-network through the proportion of hyper-triangles to paths of length two and the other characterizing the formation of triples of mutually adjacent groups in the hyper-network. All of these characteristics are studied in two different hyper-networks; a scientific collaboration hyper-network and an ecological competence hyper-network.

16 pages, 3 figures

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• A Survey on Centrality Metrics and Their Implications in Network Resilience
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• Higher order molecular organisation as a source of biological function
• Epidemics on Hypergraphs: Spectral Thresholds for Extinction
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• The Aging Effect in Evolving Scientific Citation Networks
• Spectral Detection of Simplicial Communities via Hodge Laplacians
• Functional centrality in graphs
• Brand effect versus competitiveness in hypernetworks
• Hypergraphs: an introduction and review
• Networks of Collaborations: Hypergraph Modeling and Visualisation
• A framework to generate hypergraphs with community structure
• Asymptotic enumeration of sparse uniform hypergraphs with given degrees
• The Evolution of Hyperedge Cardinalities and Bose-Einstein Condensation in Hypernetworks
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• Measuring dynamical systems on directed hyper-graphs
• Geometry and symmetry in biochemical reaction systems
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• Spectra of hyperstars on public transportation networks
• A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks
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• Model-based clustering in simple hypergraphs through a stochastic blockmodel
• Clustering Coefficient Reflecting Pairwise Relationships within Hyperedges
• Phase transition in a power-law uniform hypergraph
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• Synchronization of an evolving complex hyper-network
• Evolution of Real-world Hypergraphs: Patterns and Models without Oracles
• Evolution of citation networks with the hypergraph formalism
• Centrality of nodes in Federated Byzantine Agreement Systems
• Mean Field Analysis of Hypergraph Contagion Model