Higher-order Network Analysis Takes Off, Fueled by Classical Ideas and New Data

Abstract

Higher-order network analysis uses the ideas of hypergraphs, simplicial complexes, multilinear and tensor algebra, and more, to study complex systems. These are by now well established mathematical abstractions. What's new is that the ideas can be tested and refined on the type of large-scale data arising in today's digital world. This research area therefore is making an impact across many applications. Here, we provide a brief history, guide, and survey.

arXiv commentBased on the SIAM News online article https://sinews.siam.org/Details-Page/higher-order-network-analysis-takes-off-fueled-by-old-ideas-and-new-data

References in corpus (6)

• Higher-order organization of complex networks
• Spectral redemption: clustering sparse networks
• Memory in network flows and its effects on spreading dynamics and community detection
• Multi-body Interactions and Non-Linear Consensus Dynamics on Networked Systems
• Block Models and Personalized PageRank
• A framework for second order eigenvector centralities and clustering coefficients

Cited by in corpus (5)

• The physics of higher-order interactions in complex systems
• What are higher-order networks?
• Hypergraph assortativity: a dynamical systems perspective
• Hypergraph Dissimilarity Measures
• Local Hyper-Flow Diffusion