Topological exploration of chemical hypergraphs using Information theory
DOI:
https://doi.org/10.31349/SuplRevMexFis.6.011315Keywords:
Shannon entropy, Mutual information, Network entropy, Chemical hypergraphAbstract
A chemical hypergraph represents a set of chemical reactions. Hypernodes consist of sets of substances that act as reactants or products, while hyperedges correspond to chemical reactions, linking reactants to products. Another key structure in the hypergraph is the intersection of hypernodes, representing substances that participate in multiple reactions. In this work, we study a random walker on a chemical hypergraph under two different transition probability regimes. We characterize the random walker using network entropy, highlighting differences between these regimes. Additionally, we examine the structure of hypernodes by defining chemically inspired random variables and analyzing their joint and marginal Shannon entropies, as well as their mutual information. For large N, we observe bounds in these quantities.
References
N. Biggs, Algebraic graph theory, 67, (1993), Cambridge university press.
M. Barthélemy, Spatial networks, Physics reports, 499, 1-3, (2011), Elsevier.
M. Newman, Networks, (2018), Oxford university press.
A. Bretto, Hypergraph theory, An introduction. Mathematical Engineering. Cham: Springer, 1, 209-216, (2013), Springer.
A. García-Chung, M. Bermúdez-Montaña, P. F. Stadler, J. Jost, and G. Restrepo, Chemically inspired Erdös-Rényi oriented hypergraphs, J. Math. Chem., 62, 1357 (2024). https://doi.org/10.1007/s10910-024-01595-8
J. Jost, R. Mulas, Hypergraph Laplace operators for chemical reaction networks, Advances in mathematics, 351, 870-896, (2019), Elsevier.
F. Betancourt-Moreno, et. al., Oriented Erdős–Rényi Hypergraphs: A Computational Analysis. In progress.
E. J. Llanos, W. Leal, D. H. Luu, J. Jost, P. F. Stadler, G. Restrepo, Exploration of the chemical space and its three historical regimes, Proc. Natl. Acad. Sci. U.S.A. 116, 12660 (2019). https://doi.org/10.1073/pnas.1816039116
C. G. S. Freitas, A. L. L. Aquino, H. S. Ramos, A. C. Frery and O. A. Rosso, A detailed characterization of complex networks using Information Theory, Sci. Rep. 9, 16689 (2019). https://doi.org/10.1038/s41598-019-53167-5
C. E. Shannon, A mathematical theory of communication, Bell Syst. Tech. J. 27, 379 (1948). https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
T. M. Cover, J. A. Thomas, Elements of Information Theory (Wiley, NewYork, 1991).
S. Kullback, R. A. Leibler, On information and sufficiency, Ann. Math. Stat. 22, 79 (1951). https://doi.org/10.1214/aoms/1177729694
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 H. Laguna, Á. García Chung, F. Betancourt, G. Restrepo
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Suplemento de la Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
