Related Experiment Video
Updated: Nov 9, 2025
08:51
Statistical Modelling of Cortical Connectivity Using Non-invasive Electroencephalograms
Published on: November 1, 2019
5.8K
Optimisation of the coalescent hyperbolic embedding of complex networks
Bianka Kovács1, Gergely Palla2,3,4
1Department of Biological Physics, Eötvös Loránd University, Pázmány P. stny. 1/A, Budapest, 1117, Hungary.
Scientific Reports
|April 17, 2021
Summary
Researchers explored hyperbolic geometry in network analysis, finding a latent hyperbolic space. They optimized hyperbolic embedding algorithms, improving network structure analysis and data representation.
Area of Science:
- Network Science
- Complex Systems
- Hyperbolic Geometry
Background:
- Real-world networks exhibit properties suggesting an underlying hyperbolic geometry.
- The popularity-similarity optimization (PSO) model generates networks with scale-free, high-clustering, and small-world properties.
Purpose of the Study:
- To develop improved hyperbolic embedding algorithms for network analysis.
- To enhance the accuracy and efficiency of inferring hyperbolic coordinates from network structures.
Main Methods:
- Utilized the noncentered minimum curvilinear embedding (ncMCE) framework.
- Proposed an optimization for angular coordinates within the ncMCE method.
Main Results:
- The optimized ncMCE method reduced logarithmic loss.
- The enhanced approach improved the greedy routing score of hyperbolic embeddings.
- Achieved higher quality inferred hyperbolic coordinates.
Conclusions:
- The proposed angular coordinate optimization offers significant improvements to hyperbolic embedding quality.
- This advancement enhances the intuitive understanding and analysis of complex network structures.
Related Concept Videos
01:17Graphs of Polar Equations
75
The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...
75
01:30Geometry of Hyperbolas
65
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...
65
01:19Routh-Hurwitz Criterion II
575
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
575
01:24Sequence Networks of Rotating Machines
269
A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
Zero-sequence current induces a voltage drop across the generator's neutral impedance and other...
269
01:30Hyperbolas
50
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 axis...
50
01:15Routh-Hurwitz Criterion I
388
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
388