Higher-order interaction networks

Guest Edited by Prof Ginestra Bianconi (Queen Mary University) in collaboration with our Editorial Board Member Prof Federico Battiston (Central European University).

Many real-world systems, from social relationships to the human brain, can be successfully described as graphs: a collection of elementary units (nodes), and their pairwise interactions (links). Over the years, network approaches have been successfully applied to a wide class of domains, from economics to ecology. Thanks to technological advances and an increasingly interconnected world, data availability has recently exploded, amplifying the potential and applicability of network science approaches. Despite being widespread, traditional network descriptions often do not provide a faithful representation of reality. In many systems, interactions among the units are not limited to pairs, but can occur in groups of greater size. This is the case of human face-to-face interactions, species interactions in an ecosystem, or neurological coupling among different brain regions. These ‘higher-order interactions’ are better described by simplicial complexes and hypergraphs, more complex mathematical structures with respect to traditional graphs.

Building on early mathematical work on topological data analysis and graph theory, and supported by new experimental evidence, the investigation of networks with higher-order interactions has become ubiquitous in the last decade. Taking into account the higher-order structure of real-world systems has revealed new patterns of interactions and functionality which arise from inherently high-order features and could not be understood by limiting the analysis of structural properties to pairwise links. From social contagion to synchronisation, the introduction of higher-order interactions in networked systems has already been shown to give rise to new emergent physical phenomena, which cannot be predicted by breaking higher-order interactions into simple low-order dyads. 

The aim of this Collection is to provide, as a single resource, a venue for the latest and most important findings on higher-order interaction networks, which we believe will become an important reference for physicists working on the topic in the future years.

artistic representation of higher order interactions between nodes

Published articles