A Proposal for Network HyperTopology and Super-hypertopology: A Framework for Multi-Level Network Structures
Keywords:
HyperStructure, SuperHyperStructure, Network Topology, Network HyperTopology , Network Super-hypertopology, NetworkAbstract
We introduce the notions of {Network Hypertopology} and {Network Super-hypertopology}, which extend the classical graph‐based model of network topology to higher‐order structures on its power sets. A network topology $G=(V,E)$ encodes connectivity, directionality, and link metrics among devices. By endowing the hyperspace $\mathcal{P}(V)$ with the Vietoris (hypertopology) topology, we lift these closure axioms to families of node‐sets. Iterating this construction across iterated power sets $\mathcal{P}^n(V)$ yields a {Super-hypertopology} that maintains arbitrary‐union and finite‐intersection closure at every level. While we establish the formal definitions and foundational properties of these higher‐order topologies, their practical applications and empirical evaluation remain open for future investigation.References
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Data Availability Statement
No data were generated or analyzed in the course of this theoretical investigation. We encourage future
empirical studies to test and extend the ideas presented here.
