Networks beyond pairwise interactions: structure and dynamics

Abstract

The complexity of many biological, social and technological systems stems from the richness of the interactions among their units. Over the past decades, a great variety of complex systems has been successfully described as networks whose interacting pairs of nodes are connected by links. Yet, in face-to-face human communication, chemical reactions and ecological systems, interactions can occur in groups of three or more nodes and cannot be simply described just in terms of simple dyads. Until recently, little attention has been devoted to the higher-order architecture of real complex systems. However, a mounting body of evidence is showing that taking the higher-order structure of these systems into account can greatly enhance our modeling capacities and help us to understand and predict their emerging dynamical behaviors. Here, we present a complete overview of the emerging field of networks beyond pairwise interactions. We first discuss the methods to represent higher-order interactions and give a unified presentation of the different frameworks used to describe higher-order systems, highlighting the links between the existing concepts and representations. We review the measures designed to characterize the structure of these systems and the models proposed in the literature to generate synthetic structures, such as random and growing simplicial complexes, bipartite graphs and hypergraphs. We introduce and discuss the rapidly growing research on higher-order dynamical systems and on dynamical topology. We focus on novel emergent phenomena characterizing landmark dynamical processes, such as diffusion, spreading, synchronization and games, when extended beyond pairwise interactions. We elucidate the relations between higher-order topology and dynamical properties, and conclude with a summary of empirical applications, providing an outlook on current modeling and conceptual frontiers.

arXiv commentAccepted for publication in Physics Reports. 109 pages, 47 figures

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• Coevolutionary Dynamics of Group Interactions: Coevolving Nonlinear Voter Models
• Random multi-player games
• Time delay embeddings to characterize the timbre of musical instruments using Topological Data Analysis: a study on synthetic and real data
• Inference and Visualization of Community Structure in Attributed Hypergraphs Using Mixed-Membership Stochastic Block Models
• On the convergence of nonlinear averaging dynamics with three-body interactions on hypergraphs
• From Nodes to Edges: Edge-Based Laplacians for Brain Signal Processing
• Average shortest-path length in word-adjacency networks: Chinese versus English
• Uplifting edges in higher order networks: spectral centralities for non-uniform hypergraphs
• Consensus from group interactions: An adaptive voter model on hypergraphs
• A local algorithm and its percolation analysis of bipartite $z$-matching problem
• HOI-Brain: a novel multi-channel transformers framework for brain disorder diagnosis by accurately extracting signed higher-order interactions from fMRI
• Hypercontact semilattices
• Generalizing Egocentric Temporal Neighborhoods to probe for spatial correlations in temporal networks and infer their topology
• Sampling nodes and hyperedges via random walks on large hypergraphs
• The relevance of higher-order ties
• A General View on Double Limits in Differential Equations
• Connected components in networks with higher-order interactions
• Distinguishing pairwise and higher-order interactions in coupled oscillators from time series
• Kaleidoscopic reorganization of network communities across different scales
• Superstable Geometry in Triadic Percolation
• On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model
• Construction of simplicial complexes with prescribed degree-size sequences
• Household Bubbling Strategies for Epidemic Control and Social Connectivity
• Irregular Metamaterial Networks
• Heterogeneous Network Topology Induces the Widom Line
• Topological measures in weighted hypergraphs
• Anomalous finite-size scaling in higher-order processes with absorbing states
• Identifying maximal sets of significantly interacting nodes in higher-order networks
• Dynamical systems defined on simplicial complexes: symmetries, conjugacies, and invariant subspaces
• Planted matching problems on random hypergraphs
• Phase transitions for polyadic epidemic and voter models with multiscale groups
• Hypergraphs from multivariate connectivity: caCOH-based EEG/MEG representation
• Diagrammatics of free energies with fixed variance for high-dimensional data
• Non-exchangeable evolutionary and mean field games and their applications
• Detecting Patterns of Interaction in Temporal Hypergraphs via Edge Clustering
• Robustness of complexity estimation in event-driven signals against accuracy of event detection method
• Statistical properties of mutualistic-competitive random networks
• Latent geometry emerging from network-driven processes
• Exploring the space of graphs with fixed discrete curvatures
• Deterministic simplicial complexes
• Community Integration Algorithms (CIAs) for Dynamical Systems on Networks
• Magnetization of electronic ground states in frustrated superstable graphs
• Homogeneous coupled cell systems with high-dimensional internal dynamics
• Uncovering the non-equilibrium stationary properties in sparse Boolean networks
• Ivanova contact join-semilattices are not finitely axiomatizable
• Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks
• Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs
• Preferential attachment hypergraph with vertex deactivation