Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Graphical Representation of Inequalities01:28

Graphical Representation of Inequalities

445
The graph of the equation where y equals x squared forms a curve known as a parabola. This curve acts as a boundary in the coordinate plane, dividing it into distinct regions based on the relative position of points.When the equality sign in the equation is replaced with an inequality—such as greater than, less than, greater than or equal to, or less than or equal to—the graphical representation changes from a single curve into a broader shaded area that signifies the set of all...
445
Graphs of Equations in Two Variables01:30

Graphs of Equations in Two Variables

423
An equation with two variables, typically written in the form y = f(x) or Ax + By = C, describes a relationship between quantities represented by x and y. Each solution to such an equation is an ordered pair (x, y) that satisfies the equation when substituted. These pairs can be represented graphically to understand the variables' relationship visually.A common technique for constructing the graph of a two-variable equation is to create a value table. Begin by choosing several values for the...
423
Graphs of Functions01:30

Graphs of Functions

548
Graphs of functions provide a visual representation of how output values change in response to varying inputs. Each point on the graph corresponds to an ordered pair, where the x-coordinate (independent variable) determines the horizontal position and the y-coordinate (dependent variable) determines the vertical position. Linear functions like y = x give a straight line, indicating a constant rate of change.Nonlinear functions display more complex behaviors. Even power functions generate...
548
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

1.3K
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...
1.3K
Graphs of Polar Equations01:17

Graphs of Polar Equations

457
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...
457
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

13.7K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
13.7K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Screening for Left Ventricular Hypertrophy Using Artificial Intelligence Algorithms Based on 12 Leads of the Electrocardiogram-Applicable in Clinical Practice?-Critical Literature Review with Meta-Analysis.

Healthcare (Basel, Switzerland)·2025
Same author

Are There Limits in Explainability of Prognostic Biomarkers? Scrutinizing Biological Utility of Established Signatures.

Cancers·2021
Same author

Impact of information diffusion on epidemic spreading in partially mapping two-layered time-varying networks.

Nonlinear dynamics·2021
Same author

Limitations of Explainability for Established Prognostic Biomarkers of Prostate Cancer.

Frontiers in genetics·2021
Same author

Ensuring the Robustness and Reliability of Data-Driven Knowledge Discovery Models in Production and Manufacturing.

Frontiers in artificial intelligence·2021
Same author

Data-Driven Computational Social Network Science: Predictive and Inferential Models for Web-Enabled Scientific Discoveries.

Frontiers in big data·2021

Related Experiment Video

Updated: Apr 27, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

4.7K

Structural differentiation of graphs using Hosoya-based indices.

Matthias Dehmer1, Abbe Mowshowitz2, Yongtang Shi3

  • 1Department of Computer Science, Universität der Bundeswehr München, Neubiberg, Germany; Institute for Bioinformatics and Translational Research, UMIT, Hall in Tyrol, Austria.

Plos One
|July 15, 2014
PubMed
Summary

We introduce Hosoya-Spectral indices and Hosoya information content, novel graph theory measures. These indices combine graph spectra and partial Hosoya polynomials to analyze graph structures effectively.

More Related Videos

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.7K
Automatic Identification of Dendritic Branches and their Orientation
06:08

Automatic Identification of Dendritic Branches and their Orientation

Published on: September 17, 2021

1.8K

Related Experiment Videos

Last Updated: Apr 27, 2026

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
05:39

Generating Strictly Controlled Stimuli for Figure Recognition Experiments

Published on: March 18, 2019

4.7K
Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients
09:32

Network Analysis of Foramen Ovale Electrode Recordings in Drug-resistant Temporal Lobe Epilepsy Patients

Published on: December 18, 2016

13.7K
Automatic Identification of Dendritic Branches and their Orientation
06:08

Automatic Identification of Dendritic Branches and their Orientation

Published on: September 17, 2021

1.8K

Area of Science:

  • Graph theory
  • Mathematical chemistry
  • Network analysis

Background:

  • Graph theory utilizes spectral properties and polynomial invariants.
  • Hosoya polynomials encode topological information about molecular graphs.
  • Existing graph invariants may lack sufficient discriminatory power for certain graph structures.

Purpose of the Study:

  • Introduce novel graph invariants: Hosoya-Spectral indices and Hosoya information content.
  • Combine graph spectra with partial Hosoya polynomials for enhanced structural analysis.
  • Develop a graph entropy measure based on vertex properties.

Main Methods:

  • Definition of Hosoya-Spectral indices integrating graph spectra and partial Hosoya polynomials.
  • Formulation of Hosoya information content based on graph blocks with identical partial Hosoya polynomials.
  • Numerical evaluation of the proposed indices' discrimination power.

Main Results:

  • The Hosoya-Spectral indices offer a new perspective by merging spectral and polynomial graph properties.
  • The Hosoya information content provides an entropy-based measure sensitive to local graph structures.
  • Numerical interpretations demonstrate the utility and discrimination capabilities of these novel graph invariants.

Conclusions:

  • Hosoya-Spectral indices and Hosoya information content are valuable additions to graph theory metrics.
  • These measures enhance the ability to distinguish between different graph structures.
  • The study provides a foundation for further applications in chemical graph theory and network analysis.