Results 31 to 40 of about 40,185 (227)
Hypernetwork science via high-order hypergraph walks
EPJ Data Science, 2020 We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width.
Sinan G. Aksoy +4 more
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Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications, 2023 Let $\mathcal{H}=(X,\mathcal{E})$ be a hypergraph. A support is a graph $Q$ on $X$ such that for each $E\in\mathcal{E}$, the subgraph of $Q$ on the elements in $E$ is connected. We consider hypergraphs defined on a host graph. Given a graph $G=(V,E)$, with $c:V\to\{\R,\B\}$ and a collection of connected subgraphs $\mathcal{H}$ of $G$, a primal support ...
Raman, Rajiv, Singh, Karamjeet
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Approximation Algorithms for Hypergraph Small Set Expansion and Small Set Vertex Expansion [PDF]
, 2014 The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.
Louis, Anand, Makarychev, Yury
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Topology and its Applications, 2011 We investigate a family of polytopes introduced by E.M.\ Feichtner, A.\ Postnikov and B.\ Sturmfels, which were named nestohedra. The vertices of these polytopes may intuitively be understood as constructions of hypergraphs. Limit cases in this family of polytopes are, on the one end, simplices, and, on the other end, permutohedra.
Došen, Kosta, Petrić, Zoran
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Inventiones mathematicae, 2015 We develop a notion of containment for independent sets in hypergraphs. For every $r$-uniform hypergraph $G$, we find a relatively small collection $C$ of vertex subsets, such that every independent set of $G$ is contained within a member of $C$, and no member of $C$ is large; the collection, which is in various respects optimal, reveals an underlying ...
Saxton, David, Thomason, Andrew
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Magic of quantum hypergraph states [PDF]
QuantumMagic, or nonstabilizerness, characterizes the deviation of a quantum state from the set of stabilizer states, playing a fundamental role in quantum state complexity and universal fault-tolerant quantum computing.
Junjie Chen, Yuxuan Yan, You Zhou
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Optimal Query Complexity for Reconstructing Hypergraphs [PDF]
, 2010 In this paper we consider the problem of reconstructing a hidden weighted hypergraph of constant rank using additive queries. We prove the following: Let $G$ be a weighted hidden hypergraph of constant rank with n vertices and $m$ hyperedges. For any $m$
Bshouty, Nader H., Mazzawi, Hanna
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Discrete Mathematics, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Barry Guiduli, Zoltán Király
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Physical Review E, 2023 Providing an abstract representation of natural and human complex structures is a challenging problem. Accounting for the system heterogenous components while allowing for analytical tractability is a difficult balance. Here I introduce complex hypergraphs (chygraphs), bringing together concepts from hypergraphs, multi-layer networks, simplicial ...
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MSHC: a multi-stage hypergraph clustering algorithm
Shenzhen Daxue xuebao. Ligong banAs a high-dimensional extension of ordinary graphs, hypergraphs can more flexibly reflect high-order complex relationships between nodes. Hypergraph clustering aims to discover complex high-order correlations in powerful hypergraph structures.
ZHANG Chunying +4 more
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