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Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature - the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.
We introduce Forman-Ricci curvature and its corresponding flow as characteristics for complex networks attempting to extend the common approach of node-based network analysis by edge-based characteristics. Following a theoretical introduction and mat
Many graph products have been applied to generate complex networks with striking properties observed in real-world systems. In this paper, we propose a simple generative model for simplicial networks by iteratively using edge corona product. We prese
A majority of real life networks are weighted and sparse. The present article aims at characterization of weighted networks based on sparsity, as a measure of inherent diversity, of different network parameters. It utilizes sparsity index defined on
Identifying the infection sources in a network, including the index cases that introduce a contagious disease into a population network, the servers that inject a computer virus into a computer network, or the individuals who started a rumor in a soc
Recently, real world networks having constant/shrinking diameter along with power-law degree distribution are observed and investigated in literature. Taking an inspiration from these findings, we propose a deterministic complex network model, which