{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T07:23:11Z","timestamp":1769152991004,"version":"3.49.0"},"reference-count":25,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T00:00:00Z","timestamp":1698710400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European University Cyprus"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We study partitions (equitable, externally equitable, or other) of graphs that describe physico-chemical systems at the atomic or molecular level; provide examples that show how these partitions are intimately related with symmetries of the systems; and discuss how such a link can further lead to insightful relations with the systems\u2019 physical and chemical properties. We define a particular kind of graph partition, which we call Chemical Equitable Partition (CEP), accounting for chemical composition as well as connectivity and associate it with a quantitative measure of information reduction that accompanies its derivation. These concepts are applied to model molecular and crystalline solid systems, illustrating their potential as a means to classify atoms according to their chemical or crystallographic role. We also cluster materials in meaningful manners that take their microstructure into account and even correlate them with the materials\u2019 physical properties.<\/jats:p>","DOI":"10.3390\/e25111504","type":"journal-article","created":{"date-parts":[[2023,10,31]],"date-time":"2023-10-31T11:16:27Z","timestamp":1698750987000},"page":"1504","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Graph Partitions in Chemistry"],"prefix":"10.3390","volume":"25","author":[{"given":"Ioannis","family":"Michos","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, School of Sciences, European University Cyprus, 6 Diogenous Str., Nicosia 2404, Cyprus"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2276-8374","authenticated-orcid":false,"given":"Vasilios","family":"Raptis","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, School of Sciences, European University Cyprus, 6 Diogenous Str., Nicosia 2404, Cyprus"},{"name":"Institute of Nanoscience and Nanotechnology, National Scientific Research Center \u2018Demokritos\u2019, Patr. Gregoriou E & 27 Neapoleos, 15341 Agia Paraskevi, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.1021\/acs.jcim.3c00445","article-title":"FunQG: Molecular Representation Learning via Quotient Graphs","volume":"63","author":"Hajiabolhassan","year":"2023","journal-title":"J. Chem. Inf. Model."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1107\/S0108767384000088","article-title":"Nomenclature and Generation of Three-Periodic Nets: The Vector Method","volume":"A40","author":"Chung","year":"1984","journal-title":"Acta Cryst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1016\/j.fmre.2021.06.005","article-title":"Enhancing crystal structure prediction by decomposition and evolution schemes based on graph theory","volume":"1","author":"Gao","year":"2021","journal-title":"Fundam. Res."},{"key":"ref_4","unstructured":"Mizutani, U. (2003). Introduction to the Electron Theory of Metals, Cambridge University Press."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Allen, M.P., and Tildesley, D.J. (2017). Computer Simulation of Liquids, Oxford University Press. [2nd ed.].","DOI":"10.1093\/oso\/9780198803195.001.0001"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1941","DOI":"10.1007\/s10910-017-0773-5","article-title":"The Toroidal Unit of a Quasicrystal","volume":"55","author":"Rosenfeld","year":"2017","journal-title":"J. Math. Chem."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"964","DOI":"10.1137\/19M1283495","article-title":"Invariant Synchrony Subspaces of Sets of Matrices","volume":"19","author":"Neuberger","year":"2020","journal-title":"SIAM J. Appl. Dyn. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/S0012-365X(03)00233-4","article-title":"Computing the average parallelism in trace monoids","volume":"273","author":"Krob","year":"2003","journal-title":"Discret. Math."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1016\/j.ejc.2005.03.006","article-title":"Laplacian eigenvectors and eigenvalues and almost equitable partitions","volume":"28","author":"Cardoso","year":"2007","journal-title":"Eur. J. Comb."},{"key":"ref_10","unstructured":"Cvetkovic, D., Doob, M., and Sachs, H. (1980). Spectra of Graphs: Theory & Application (Volume 87 of Pure and Applied Mathematics), Academic Press."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"042805","DOI":"10.1103\/PhysRevE.88.042805","article-title":"Observability and coarse graining of consensus dynamics through the external equitable partition","volume":"88","author":"Yuan","year":"2013","journal-title":"Phys. Rev. E"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Wagner, S., and Wang, H. (2019). Introduction to Chemical Graph Theory, CRC Press.","DOI":"10.1201\/9780429450532"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kittel, C. (1953). Introduction to Solid State Physics, John Wiley.","DOI":"10.1119\/1.1933590"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1038\/s42005-020-0345-z","article-title":"Exploiting Symmetries in Network Analysis","volume":"3","year":"2020","journal-title":"Commun. Phys."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Raptis, V., and Kaltzoglou, A. (2024). Graph-theoretical Analysis as an Aid in the Elucidation of Structure-Property Relations of Perovskite Materials. AIP Conf. Proc., 3030, in press.","DOI":"10.1063\/5.0193237"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Hall, S., and McMahon, B. (2005). International Tables of Crystallography. Vol. G: Definition and Exchange of Crystallographic Data, Springer.","DOI":"10.1107\/97809553602060000107"},{"key":"ref_17","unstructured":"Hahn, T. (2014). International Tables of Crystallography. Brief Teaching Edition of Vol. A: Space Group Symmetry, John Wiley & Sons."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"11777","DOI":"10.1021\/acs.jpcc.6b02175","article-title":"Optical-Vibrational Properties of the Cs2SnX6 (X = Cl, Br, I) Defect Perovskites and Hole-Transport Efficiency in Dye-Sensitized Solar Cells","volume":"120","author":"Kaltzoglou","year":"2016","journal-title":"J. Phys. Chem. C"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"8617","DOI":"10.1039\/c3dt50599e","article-title":"A cartography of the van der Waals territories","volume":"42","author":"Alvarez","year":"2013","journal-title":"Dalton Trans."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1039\/C9ME00176J","article-title":"Improving the Cd2+ detection capability of a new anionic rare earth metal-organic framework based on a [RE6 (\u03bc3-OH)8]10+ secondary building unit: An ion-exchange approach towards more efficient sensors","volume":"5","author":"Panagiotou","year":"2020","journal-title":"Mol. Syst. Des. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"van Mieghem, P. (2011). Graph Spectra for Complex Networks, Cambridge University Press.","DOI":"10.1017\/CBO9780511921681"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1021\/je010308l","article-title":"Liquid Density and Critical Properties of Hydrocarbons Estimated from Molecular Structure","volume":"47","author":"Wakeham","year":"2002","journal-title":"J. Chem. Eng. Data"},{"key":"ref_23","unstructured":"Lide, D.R. (2003). CRC Handbook of Chemistry and Physics, CRC Press. [84th ed.]."},{"key":"ref_24","unstructured":"van Krevelen, D.W. (1990). Properties of Polymers, Cambridge University Press. [3rd ed.]."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"836","DOI":"10.1109\/TNSE.2018.2875425","article-title":"Generating Graphs with Symmetry","volume":"6","author":"Klickstein","year":"2019","journal-title":"IEEE Trans. Netw. Sci. Eng."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1504\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:14:56Z","timestamp":1760130896000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/11\/1504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,31]]},"references-count":25,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["e25111504"],"URL":"https:\/\/doi.org\/10.3390\/e25111504","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,31]]}}}