{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T14:54:03Z","timestamp":1778597643539,"version":"3.51.4"},"reference-count":51,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T00:00:00Z","timestamp":1679270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The use of information\u2013theoretical methodologies to assess graph-based systems has received a significant amount of attention. Evaluating a graph\u2019s structural information content is a classic issue in fields such as cybernetics, pattern recognition, mathematical chemistry, and computational physics. Therefore, conventional methods for determining a graph\u2019s structural information content rely heavily on determining a specific partitioning of the vertex set to obtain a probability distribution. A network\u2019s entropy based on such a probability distribution is obtained from vertex partitioning. These entropies produce the numeric information about complexity and information processing which, as a consequence, increases the understanding of the network. In this paper, we study the Benes network and its novel-derived classes via different entropy measures, which are based on information functionals. We construct different partitions of vertices of the Benes network and its novel-derived classes to compute information functional dependent entropies. Further, we present the numerical applications of our findings in understanding network complexity. We also classify information functionals which describe the networks more appropriately and may be applied to other networks.<\/jats:p>","DOI":"10.3390\/sym15030761","type":"journal-article","created":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T05:46:42Z","timestamp":1679291202000},"page":"761","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Complexity Analysis of Benes Network and Its Derived Classes via Information Functional Based Entropies"],"prefix":"10.3390","volume":"15","author":[{"given":"Jun","family":"Yang","sequence":"first","affiliation":[{"name":"School of Economics and Law, Chaohu University, Chaohu 238000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Asfand","family":"Fahad","sequence":"additional","affiliation":[{"name":"Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University Multan, Multan 60800, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muzammil","family":"Mukhtar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Anees","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amir","family":"Shahzad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalnagar Campus, Bahawalnagar 62300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1549-3584","authenticated-orcid":false,"given":"Zahid","family":"Iqbal","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Institute of Southern Punjab, Multan 60800, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"key":"ref_1","unstructured":"Veldhuizen, L.T. 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