Trinque problem: covering complete graphs by plane degree-bounded hypergraphs
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Combinatorial Optimization"
DOI: 10.1007/s10878-015-9978-3
Abstract: Let $$K_n$$Kn be a complete graph drawn on the plane with every vertex incident to the infinite face. For any integers i and d, we define the (i, d)-Trinque Number of $$K_n$$Kn, denoted by $${\mathcal {T}}^d_{i}(K_n)$$Tid(Kn),… read more here.
Keywords: graphs; problem covering; covering complete; trinque problem ... See more keywords
A Note on Generalized Lagrangians of Non-uniform Hypergraphs
Sign Up to like & getrecommendations! Published in 2017 at "Order"
DOI: 10.1007/s11083-016-9385-0
Abstract: Set A⊂ℕ$A\subset {\mathbb N}$ is less than B⊂ℕ$B\subset {\mathbb N}$ in the colex ordering if max(A△B)∈B. In 1980’s, Frankl and Füredi conjectured that the r-uniform graph with m edges consisting of the first m sets… read more here.
Keywords: colex ordering; edge type; question; uniform hypergraphs ... See more keywords
Influential groups for seeding and sustaining nonlinear contagion in heterogeneous hypergraphs
Sign Up to like & getrecommendations! Published in 2022 at "Communications Physics"
DOI: 10.1038/s42005-021-00788-w
Abstract: Contagion phenomena are often the results of multibody interactions—such as superspreading events or social reinforcement—describable as hypergraphs. We develop an approximate master equation framework to study contagions on hypergraphs with a heterogeneous structure in terms… read more here.
Keywords: hypergraphs; groups seeding; nonlinear contagion; influential groups ... See more keywords
Synchronization of phase oscillators on complex hypergraphs.
Sign Up to like & getrecommendations! Published in 2022 at "Chaos"
DOI: 10.1063/5.0116747
Abstract: We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of differential equations for… read more here.
Keywords: phase oscillators; oscillators complex; phase; synchronization phase ... See more keywords
HyperGraphs.jl: representing higher-order relationships in Julia
Sign Up to like & getrecommendations! Published in 2022 at "Bioinformatics"
DOI: 10.1093/bioinformatics/btac347
Abstract: Abstract Summary HyperGraphs.jl is a Julia package that implements hypergraphs. These are a generalization of graphs that allow us to represent n-ary relationships and not just binary, pairwise relationships. High-order interactions are commonplace in biological… read more here.
Keywords: higher order; hypergraphs representing; representing higher; order relationships ... See more keywords
Complex hypergraphs
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.107.024316
Abstract: 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),… read more here.
Keywords: complex hypergraphs; hypergraphs; chygraphs;
Pathway Analysis with Signaling Hypergraphs
Sign Up to like & getrecommendations! Published in 2017 at "IEEE/ACM Transactions on Computational Biology and Bioinformatics"
DOI: 10.1109/tcbb.2015.2459681
Abstract: Signaling pathways play an important role in the cell’s response to its environment. Signaling pathways are often represented as directed graphs, which are not adequate for modeling reactions such as complex assembly and dissociation, combinatorial… read more here.
Keywords: signaling pathways; analysis signaling; signaling hypergraphs; hypergraph ... See more keywords
Accessible spectrum of graphs
Sign Up to like & getrecommendations! Published in 2021 at "Applicable Analysis and Discrete Mathematics"
DOI: 10.2298/aadm180319007h
Abstract: This paper computes eigenvalues of discrete complete hypergraphs and partitioned hypergraphs. We define positive equivalence relation on hypergraphs that establishes a connection between hypergraphs and graphs. With this regards it makes a connection between spectrum… read more here.
Keywords: spectrum graphs; graphs; hypergraphs; accessible spectrum ... See more keywords
A Poset-Based Approach to Curvature of Hypergraphs
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DOI: 10.3390/sym14020420
Abstract: In this contribution, we represent hypergraphs as partially ordered sets or posets, and provide a geometric framework based on posets to compute the Forman–Ricci curvature of vertices as well as hyperedges in hypergraphs. Specifically, we… read more here.
Keywords: hypergraphs; forman ricci; poset based; ricci curvature ... See more keywords
The critical node detection problem in hypergraphs using weighted node degree centrality
Sign Up to like & getrecommendations! Published in 2023 at "PeerJ Computer Science"
DOI: 10.7717/peerj-cs.1351
Abstract: Network analysis is an indispensable part of today’s academic field. Among the different types of networks, the more complex hypergraphs can provide an excellent challenge and new angles for analysis. This study proposes a variant… read more here.
Keywords: node detection; critical node; weighted node; node degree ... See more keywords