Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Entropy

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

Entropy

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.

Law of Independent Assortment

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.

One-Degree-of-Freedom System

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
A one-degree-of-freedom system is defined by an independent variable that determines its state and behavior. One example of a one-degree-of-freedom system is a simple harmonic oscillator, such as a...

Degrees of Freedom

Degrees of Freedom

The degree of freedom for a particular statistical calculation is the number of values that are free to vary. Thus, the minimum number of independent numbers can specify a particular statistic. The degrees of freedom differ greatly depending on known and uncalculated statistical components.
For example, suppose there are three unknown numbers whose mean is 10; although we can freely assign values to the first and second numbers, the value of the last number can not be arbitrarily assigned.

You might also read

Related Articles

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

Sort by

Same author

Dynamics of neural fields with exponential temporal kernel.

Theory in biosciences = Theorie in den Biowissenschaften·2024

Same author

Chaos in gene regulatory networks: Effects of time delays and interaction structure.

Chaos (Woodbury, N.Y.)·2024

Same author

Analytic relationship of relative synchronizability to network structure and motifs.

Proceedings of the National Academy of Sciences of the United States of America·2023

Same author

A mathematical interpretation for outbreaks of bacterial meningitis under the effect of time-dependent transmission parameters.

Nonlinear dynamics·2023

Same author

Correction to: Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy.

Nonlinear dynamics·2021

Same author

Modelling personal cautiousness during the COVID-19 pandemic: a case study for Turkey and Italy.

Nonlinear dynamics·2021

Search research articles

Related Experiment Video

Updated: Jan 22, 2026

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold

Published on: February 10, 2023

Graph entropy, degree assortativity, and hierarchical structures in networks.

Fatihcan M Atay¹, Türker Bıyıkoğlu²

¹Bilkent University, Department of Mathematics, 06800 Ankara, Turkey.

Physical Review. E

|January 21, 2026

Summary

This study reveals that graphs with maximum topological entropy exhibit a hierarchical structure, characterized by a breadth-first search ordering with decreasing degrees (BFD ordering). This structure also maximizes the Randić index and relates graph properties like assortativity and centrality measures.

More Related Videos

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

Hierarchical and Programmable One-Pot Oligosaccharide Synthesis

Hierarchical and Programmable One-Pot Oligosaccharide Synthesis

Published on: September 6, 2019

Related Experiment Videos

Last Updated: Jan 22, 2026

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold

Versatile Technique to Produce a Hierarchical Design in Nanoporous Gold

Published on: February 10, 2023

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Soft Pneumatic Robot Modulates Graph Theory Metrics of Brain Network for Hand Rehabilitation After Stroke

Published on: October 10, 2025

Hierarchical and Programmable One-Pot Oligosaccharide Synthesis

Hierarchical and Programmable One-Pot Oligosaccharide Synthesis

Published on: September 6, 2019

Area of Science:

Graph theory
Network science
Mathematical physics

Background:

Connecting structural and dynamical properties of graphs is crucial for understanding complex systems.
Topological entropy, spectral radius, Randić index, and degree assortativity are key graph metrics.
Understanding the relationship between these metrics can reveal fundamental graph structures.

Purpose of the Study:

To investigate the relationship between topological entropy, Randić index, and degree assortativity in graphs.
To characterize the structure of graphs that maximize topological entropy and the Randić index.
To explore the implications for graph centrality measures and entropy differences.

Main Methods:

Analysis of graph properties including spectral radius and adjacency matrix.
Derivation of conditions for maximum topological entropy and Randić index.
Application of breadth-first search (BFS) ordering, specifically BFD ordering.
Definition and analysis of a normalized Randić function and Shannon entropies.

Main Results:

The graph with maximum entropy for a given degree sequence has a hierarchical BFD ordering.
Maximum entropy graphs exhibit high degree assortativity, and degree and eigenvector centrality coincide.
The graph maximizing the Randić index also satisfies a BFD ordering.
A normalized Randić function's maximum value relates to Shannon entropy differences.

Conclusions:

Hierarchical structures (BFD ordering) are central to maximizing graph entropy and Randić index.
Degree assortativity and centrality measures are intrinsically linked to these structural properties.
The study provides a unified framework connecting diverse graph invariants through structural organization.