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Related Concept Videos

Hyperbolas01:30

Hyperbolas

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A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse...
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A hyperbola consists of all points where the absolute difference of distances to two fixed points, called foci, remains constant. The standard equation isEach branch extends infinitely and approaches two asymptotes, which guide the curve’s behavior. The parameters a and b define key features: a measures the distance from the center to each vertex along the transverse axis, while b influences the slopes of the asymptotes. The asymptotes have equationsA rectangle centered at the origin with...
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Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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Community detection in hypergraphs through hyperedge percolation.

Bianka Kovács1, Barnabás Benedek2, Gergely Palla3,4

  • 1Institute of Evolution, HUN-REN Centre for Ecological Research, Konkoly-Thege M. út 29-33, Budapest, 1121, Hungary.

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|October 15, 2025
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Summary
This summary is machine-generated.

We introduce novel hypergraph community detection methods, adapting k-clique percolation for complex systems. These methods offer distinct community structures compared to pairwise projections, suitable for various hypergraph types.

Keywords:
Clique percolationCommunity detectionHypergraphOverlapping communities

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Area of Science:

  • Network Science
  • Graph Theory
  • Data Mining

Background:

  • Complex networks often display community structure, where nodes are densely interconnected within groups.
  • Modeling systems with interactions involving more than two nodes requires hypergraphs, necessitating specialized community detection algorithms.

Purpose of the Study:

  • To adapt the k-clique percolation method for community detection in hypergraphs.
  • To explore two distinct hypergraph community detection algorithms and compare their performance.

Main Methods:

  • Adapted k-clique percolation to hypergraphs by defining communities based on hyperedges with at least k nodes.
  • Proposed an alternative method restricting maximum hyperedge size for community detection.
  • Compared algorithms on synthetic and real-world hypergraphs, including those from hyperbolic geometry.

Main Results:

  • Communities detected directly from hyperedges can differ from those found using the pairwise projection of the hypergraph.
  • The alternative method, restricting maximum hyperedge size, is more suitable for hypergraphs with weaker linkages represented by larger hyperedges.

Conclusions:

  • The proposed hypergraph community detection methods provide valuable tools for analyzing complex systems.
  • The choice of algorithm depends on the specific characteristics of the hypergraph, particularly hyperedge cardinality and linkage strength.