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PyTIE: A Python Program for the Evaluation of Degree-Based Topological Descriptors and Molecular Entropy

Sahaya Vijay Jeyaraj, Roy S, Govardhan S, Tony Augustine, Jyothish K

TL;DR

PyTIE tackles the need for a fast, extensible tool to compute diverse degree-based, degree-sum-based, and entropy-based topological descriptors for molecular graphs. The authors present four open-source Python packages—$PyTIE extunderscore D$, $PyTIE extunderscore DS$, $PyTIE extunderscore SMS extunderscore DE$, and $PyTIE extunderscore SMS extunderscore DSE$—that achieve constant-time computations and integrate with $NumPy$, $Math$, and $SymPy$. They demonstrate the approach with kekulene tessellations, validate against manual calculations, and extend the framework to enthalpy estimations using edge-distribution methods, underscoring practical impact for QSAR/QSPR and materials design. Overall, PyTIE provides a cross-platform, community-friendly resource that accelerates descriptor-based modeling and supports future machine-learning applications in molecular property prediction.

Abstract

We have developed PyTIE (Python Topological Indices Expressions) which is defined as the collections of Python packages such as PyTIE D, PyTIE DS, PyTIE SMS DE, and PyTIE SMS DSE, which are open-source software packages and cross-platform Python package designed to expedite the retrieval of results for mathematics, chemistry and chemical engineering researchers within constant time. This open-source tool extends its utility to chemistry and chemical engineering researchers with limited mathematical proficiency. PyTIE facilitates the loading of molecular graphs, specifying parameters such as minimum degree, maximum degree, and the number of vertex pairs (edge partitions). The edge partitions of a molecular graph based on degree sum also plays a crucial role in predicting heat of formation and enthalpy of formation along with DFT techniques. It systematically computes expressions and numerical values for various topological indices, including degree-based and neighborhood degree-based indices, as well as Shannon's entropy, providing visual representations of the results. Emphasizing topological indices for Quantitative Structure-Activity Relationship and Quantitative Structure-Property Relationship analyses, PyTIE proves particularly relevant in these studies. Serving as a Python package, it seamlessly integrates with libraries such as NumPy, math and SymPy offering extensive options for data analysis. The efficiency of PyTIE is demonstrated through illustrative examples in various contexts.

PyTIE: A Python Program for the Evaluation of Degree-Based Topological Descriptors and Molecular Entropy

TL;DR

PyTIE tackles the need for a fast, extensible tool to compute diverse degree-based, degree-sum-based, and entropy-based topological descriptors for molecular graphs. The authors present four open-source Python packages—, , , and —that achieve constant-time computations and integrate with , , and . They demonstrate the approach with kekulene tessellations, validate against manual calculations, and extend the framework to enthalpy estimations using edge-distribution methods, underscoring practical impact for QSAR/QSPR and materials design. Overall, PyTIE provides a cross-platform, community-friendly resource that accelerates descriptor-based modeling and supports future machine-learning applications in molecular property prediction.

Abstract

We have developed PyTIE (Python Topological Indices Expressions) which is defined as the collections of Python packages such as PyTIE D, PyTIE DS, PyTIE SMS DE, and PyTIE SMS DSE, which are open-source software packages and cross-platform Python package designed to expedite the retrieval of results for mathematics, chemistry and chemical engineering researchers within constant time. This open-source tool extends its utility to chemistry and chemical engineering researchers with limited mathematical proficiency. PyTIE facilitates the loading of molecular graphs, specifying parameters such as minimum degree, maximum degree, and the number of vertex pairs (edge partitions). The edge partitions of a molecular graph based on degree sum also plays a crucial role in predicting heat of formation and enthalpy of formation along with DFT techniques. It systematically computes expressions and numerical values for various topological indices, including degree-based and neighborhood degree-based indices, as well as Shannon's entropy, providing visual representations of the results. Emphasizing topological indices for Quantitative Structure-Activity Relationship and Quantitative Structure-Property Relationship analyses, PyTIE proves particularly relevant in these studies. Serving as a Python package, it seamlessly integrates with libraries such as NumPy, math and SymPy offering extensive options for data analysis. The efficiency of PyTIE is demonstrated through illustrative examples in various contexts.

Paper Structure

This paper contains 14 sections, 3 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Result and Discussion
  4. PyTIE Features
  5. PyTIE Structures
  6. Utilizing PyTIE
  7. Topological indices, neighborhood topological indices and Shannon entropy
  8. Topological indices:
  9. Neighborhood topological descriptors:
  10. Shannon entropy:
  11. Examples of PyTIE
  12. Python module of Degree-based topological indices of $G$
  13. Robust Calculations of Enthalpies and Relative Stabilities using Bond (Edge) Distributions of Triangular and Rhomboidal Kekulenes
  14. Conclusion

Figures (4)

  • Figure 1: Molecular graph of tessellations of kekulenes (G)
  • Figure 2: Molecular graph of tessellations of kekulenes a) Stage-1 of G b) Stage-2 of G
  • Figure 3: Molecular graph of tessellations of kekulenes a) Stage-3 of G b) Stage-4 of G
  • Figure 4: Molecular graph of tessellations of kekulenes (Stage-n of G)