Evolution of coauthorship networks in view of simplicial complex

Graph, composed of nodes and links, is a simple representation for constituents and pairwise interactions, respectively. This simple method was successful for explaining diverse properties of complex systems to some extent. Hypergraph including simplicial complex is a generalization of graph, which takes into account of more than pairwise interactions between multiple nodes. Here, using this simplicial complex representation based on algebraic topology, we consider the evolution of coauthorship networks, a prototypical example of large-scale social relationships, based on empirical datasets on specific subfields in science. We found that the facet degree distribution exhibits power-law decaying behavior more elaborately than the graph degree distribution, and the first Betti number is useful for representing the emergence of a large-scale cooperative phenomenon. Moreover, we construct a model to reproduce such results, which would be useful for understanding further structural properties of such simplex complexes.