2024/02/09 by Zhaohua Guo, Rui Miao, Guo, Zhaohua +7
Computer Science · Mathematics · #Commutative Algebra and Its Applications #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Physics and Society (physics.soc-ph) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2402.06451
openalex publication_date 2024/02/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A simplex-based network is referred to as a higher-order network, in which describe that the interactions can include more than two nodes. Many multicomponent interactions can be grasped through simplicial complexes, which have recently found applications in social, technological, and biological contexts. The paper first proposes a competitive evolving model of higher-order networks. We introduce the difference equation analysis approach in the high-order network to make the analysis network more rigorous. It avoids the assumption that the degrees of nodes are continuous in the traditional analysis network. We obtain an analytical expression for the distribution of higher-order degrees by employing the theory of Poisson processes. The established results indicate that in a d-order network the scale-free behavior for the (d-1)-dim simplex with respect to the d-order degree is controlled by the competitiveness factor. As the competitiveness increases, the d-order degree of the (d-1)-dim simplex is bent under the logarithmic coordinates. While the e(