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Investigating Protein Sequence-structure-dynamics Relationships with Bio3D-web

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Degree-Based Graph Entropy in Structure-Property Modeling.

Sourav Mondal^1,2, Kinkar Chandra Das¹

¹Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea.

Entropy (Basel, Switzerland)

|July 29, 2023

Summary

This summary is machine-generated.

This study introduces second-degree-based graph entropy (Id,2) for analyzing molecular structures. This new measure, derived from graph theory, offers insights into network complexity and molecular properties.

Keywords:

QSPR analysis chemical graph theory entropy molecular graph topological index

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Area of Science:

Graph Theory
Network Analysis
Cheminformatics

Background:

Graph entropy quantifies network complexity and structural information.
Existing degree-based entropies, particularly for k=1, are well-established.
The first Zagreb index, a graph invariant, relates to the denominator in the entropy formula.

Purpose of the Study:

To introduce and investigate the second-degree-based graph entropy (Id,2).
To explore the utility of Id,2 in modeling molecular structure-property relationships.
To extend the application of degree-based graph entropies.

Main Methods:

Definition of k-th degree-based graph entropy: Id,k(G) = -∑(dG(vi)^k)/∑(dG(vj)^k) * log((dG(vi)^k)/∑(dG(vj)^k)).
Focus on the specific case k=2 for the second-degree-based entropy.
Application of Id,2 to molecular structure analysis.

Main Results:

The proposed second-degree-based entropy (Id,2) is formally defined.
The study establishes Id,2 as a potentially valuable tool for structure-property modeling.
The relationship between Id,2 and molecular complexity is highlighted.

Conclusions:

Second-degree-based graph entropy (Id,2) presents a novel metric for network and molecular analysis.
Id,2 offers a new avenue for understanding molecular structure-property relationships.
Further research into Id,2 and its applications is warranted.