Simplicial Complexes and Higher-Order Networks

Dear Colleagues,

Traditional networks are agglomerates of dyads or pairs that combine to give rise to large, interconnected webs. Although there are numerous paths that can be chosen to form groups out of pairwise connected individuals, the theoretical framework is inherently limited and awkward where it might matter the most, namely when we study group interactions. Indeed, group interactions emerge in a broad variety of social, biological, and technological systems. The remedy is indeed simple but, as past research has already shown, has far reaching consequences. In particular, let the link no longer be bound to connecting just two nodes. By allowing this, we can have links connecting 3, 7, or even 150 nodes all at once. By doing so, we enter into the realm of simplicial complexes and higher-order networks, where 'higher-order' refers to the very fact that links no longer connect just pairs but can directly connect many more nodes of a network. We thus have a theoretical framework to uniquely describe groups by means of a single link, and we can also define the links between different groups or between particular nodes of groups that form the network.

Although the potential impact of simplicial complexes and higher-order networks has already been recognized, interest in these peaked only recently, with mounting inability to converge on what constitutes a group or how to consistently define it in the realm of traditional network science. This ineptitude comes to a head when we study peer pressure, public cooperation, complex contagion, or opinion formation, to name just some examples that clearly extend well beyond pairwise interactions. More generally, however, almost every human interaction sometimes involves more than two people, thus creating an inherent need for the introduction of higher-order structures. Although past research has often successfully leveraged the language of pairwise networks to describe higher-order interactions, a paradigm shift in the way we model interactions in groups is well under way. We therefore believe that the timing of this Special Issue dedicated to simplicial complexes and higher-order networks is perfect, and we hope to receive many interesting contributions on topics such as:

• Diffusion of information
• Dismantling and immunization
• Trust, trustworthiness, and honesty
• Evolution of cooperation
• Trust and ultimatums
• Epidemic spreading
• Opinion formation
• Peer pressure

Prof. Dr. Matjaz Perc
Dr. Dibakar Ghosh
Guest Editors

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• diffusion of information
• dismantling and immunization
• trust, trustworthiness, and honesty
• evolution of cooperation
• trust and ultimatums
• epidemic spreading
• opinion formation
• peer pressure