Hypergraph Theory

Bretto, Alain

doi:10.1007/978-3-319-00080-0

Cited by 331 publications

(84 citation statements)

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“…b Definitions of hypergraphs given in the literature may differ slightly from author to author. For instance, Bretto's hypergraph definition [10] is identical to ours, apart from prohibiting empty edges (e i such that e i = ∅). Berge [11] similarly prohibits empty edges, as well as isolated vertices…”

Section: Preliminariesmentioning

confidence: 99%

Hypernetwork science via high-order hypergraph walks

et al. 2020

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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. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.

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Section: Preliminariesmentioning

confidence: 99%

Hypernetwork science via high-order hypergraph walks

et al. 2020

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“…Hypergraphs largely came to prominence along with developments in computer science. The increasing need to model more complex information relationships, such as data structures and computer networks, necessitated a more general formulation of traditional graph theory in discrete mathematics to model the more complex systems (see Berge 1973Berge , 1984Berge & Ray-Chaudhuri 2006;Bretto 2013).…”

Section: Comprehension Of Complex Sets With Hypergraphsmentioning

confidence: 99%

“…Aside from the mathematical methods and implications, hypergraphs also provide a powerful visualization tool for sets of complex relationships (see Bahmanian & Šajna 2015;Bretto 2013;Paquette & Tokuyasu 2011;Zhou, Huang, & Schölkopf 2007). Since vertices and edges (also known as links) represent set elements and set relationships between groups of those elements, a hypergraph can visually convey complexities in the organizing structures within intersecting data.…”

Section: Comprehension Of Complex Sets With Hypergraphsmentioning

confidence: 99%

Sets, Graphs, and Things We Can See: A Formal Combinatorial Ontology for Empirical Intra-Site Analysis

Cardinal

2019

Journal of Computer Applications in Archaeology

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A critical aspect of analysing an archaeological site is identifying the network of relationships between the things we find and the locations where we find them. These associations are typically determined by a combination of quantitative analyses and the professional knowledge and intuition of the archaeologist, but where exactly is the boundary between what is truly empirical field data and what is inferred through our prior knowledge and field methods? How can we best support those inferences? This paper is a critical evaluation of that boundary to firmly ground, as much as possible, a quantitative analysis on only that which we can directly observe-the thing and its location-and derive associations from that basis alone. To do so, the approach described here relies on a combination of set and graph theories rather than statistical or spatial methods. This revised ontology allows a formalization, in combinatorial terms, for describing an underlying structure to contexts and assemblages that suggests a clear association between archaeological site analysis and a well-studied class of set and graph covering problems. This, in turn, points towards potential algorithmic solutions for a more holistic parsing of the total relationships between sites, contexts, assemblages, proveniences, and artefacts.

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“…In order to solve the model above, the hypergraph theory is used. The definitions about hypergraph are explained in detail in [6], so we do not reiterate them here. We establish such a hypergraph that every vertex of represents a road link on the road network.…”

Section: Max ∑ { ′ >0} =1mentioning

confidence: 99%

Networked Monitoring of Urban Traffic Emissions

Zerui¹,

Kang²,

Jin-yi³

et al. 2019

IJESD

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This paper presents some key points for networked monitoring of urban traffic emissions. Firstly, we introduce the remote sensing devices distributed on the urban roads to measure the emissions of passing vehicles. Secondly, we discuss how to determine the device locations by maximizing the amount of the captured vehicles. Finally, a method to identify high-emitting vehicles is proposed based on broad learning system. The experiment results show the networked monitoring system is able to inspect massive on-road vehicles in a short-term and accurately identify high-emitting vehicles.

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Hypergraph Theory

Cited by 331 publications

References 0 publications

Hypernetwork science via high-order hypergraph walks

Hypernetwork science via high-order hypergraph walks

Sets, Graphs, and Things We Can See: A Formal Combinatorial Ontology for Empirical Intra-Site Analysis

Networked Monitoring of Urban Traffic Emissions

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