Modeling and analysis of higher-order interactions in collaborative networks

Interactions between the individuals involved in a complex collaborative network cannot always be accurately described by pairwise relations alone. We survey the literature on such systems, where higher-order (beyond pairwise) relations between the components are necessary to capture the nature of the entire system. We are particularly interested in the applications of the simplicial complex model, in which the fact that a group of individuals as a whole (e.g. {Alice, Bob, Carol}) is in the relation, implies that all smaller subsets of this group are in the same relation. However, we do not limit ourselves to only this model, and also consider hypergraphs, bipartite graphs, and graph module decompositions, if they work better in a particular case. We review a broad range of networks that possess high-order interactions: scientific co-authorship, social networks, biological examples such as protein-protein interactions and species co-occurrence. Since we are specifically interested in the simplicial complex model, we also give a brief review on computing their topological properties such as Betti numbers, and describe some standard geometric complexes (Cech and Vietoris-Rips). Then we consider the applications to games, and the concepts of joint information and correlation. After that, we talk about computational aspects on using simplicial complexes, specialized data structures and algorithms, such as the simplex tree data structure.