Homological percolation transitions in evolving coauthorship complexes

Simplicial complex representation (SCR) is an elegant framework for expressing social relationships, including high-order interactions. Using SCR, we explore the homological percolation transitions (HPTs) of evolving coauthorship complexes based on empirical datasets. The HPTs are determined by the first and second Betti numbers, which indicate the appearance of one and two dimensional macroscopic-scale homological cycles and cavities, respectively. A minimal simplicial-complex model is proposed, which has two essential factors, growth and preferential attachment. This model successfully reproduces the HPTs and determines the transition types as infinite order (the Berezinskii-Kosterlitz-Thouless type), with different critical exponents. In contrast to Kahle localization, the first Betti number maintains increasing even after the second Betti number appears. This delocalization stems from the two factors and thus arises when the merging rate of 2-dimensional simplexes is less than the birth rate of isolated simplexes. Our results provide topological insight into the maturing steps of social networks.