Due to their ability to express higher-order structures, hypergraphs are becoming a central topic in network analysis. In this paper, we propose a parameter-free clique centrality index for all the hypergraphs, including hypergraphs involving singleton hyperedges and disconnected hypergraphs. We construct a hereditary class by introducing the null simplex into the simplicial complex of a hypergraph. Summarizing the boundary–coboundary relations in the hereditary complex, the hereditary diagram is defined and naturally connected. Inner and outer centrality indices are defined for all simplices with respect to the dual relations of the coboundary and boundary, respectively, and made into a global circuit whose steady state defines the Hereditary DualRank centrality. Based on the ratio of the outer and inner centralities of a simplex, we define its effectiveness, which describes the relative productivity of the corresponding clique. Applying the Hereditary DualRank centrality to a scientific collaboration dataset, we analyze individual choices in collaborations, reflecting, in detail, the trend that scholars seek for relatively effective cooperations in upcoming research. Based on the individual effectiveness values, we define the efficiency index of collaboration and reveal its negative correlation with the dispersity of individual effectiveness values. This work offers an in-depth topological understanding of the evolution and dynamics of hypergraphs.
Liu et al. (Fri,) studied this question.