{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:42:17Z","timestamp":1760143337085,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T00:00:00Z","timestamp":1706659200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LQ22F030008","61873080","2021QDL030"],"award-info":[{"award-number":["LQ22F030008","61873080","2021QDL030"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LQ22F030008","61873080","2021QDL030"],"award-info":[{"award-number":["LQ22F030008","61873080","2021QDL030"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific Research Foundation for Scholars of HZNU","award":["LQ22F030008","61873080","2021QDL030"],"award-info":[{"award-number":["LQ22F030008","61873080","2021QDL030"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Analyzing and characterizing the differences between networks is a fundamental and challenging problem in network science. Most previous network comparison methods that rely on topological properties have been restricted to measuring differences between two undirected networks. However, many networks, such as biological networks, social networks, and transportation networks, exhibit inherent directionality and higher-order attributes that should not be ignored when comparing networks. Therefore, we propose a motif-based directed network comparison method that captures local, global, and higher-order differences between two directed networks. Specifically, we first construct a motif distribution vector for each node, which captures the information of a node\u2019s involvement in different directed motifs. Then, the dissimilarity between two directed networks is defined on the basis of a matrix, which is composed of the motif distribution vector of every node and the Jensen\u2013Shannon divergence. The performance of our method is evaluated via the comparison of six real directed networks with their null models, as well as their perturbed networks based on edge perturbation. Our method is superior to the state-of-the-art baselines and is robust with different parameter settings.<\/jats:p>","DOI":"10.3390\/e26020128","type":"journal-article","created":{"date-parts":[[2024,1,31]],"date-time":"2024-01-31T08:44:06Z","timestamp":1706690646000},"page":"128","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Directed Network Comparison Using Motifs"],"prefix":"10.3390","volume":"26","author":[{"given":"Chenwei","family":"Xie","sequence":"first","affiliation":[{"name":"Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiao","family":"Ke","sequence":"additional","affiliation":[{"name":"Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haoyu","family":"Chen","sequence":"additional","affiliation":[{"name":"Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chuang","family":"Liu","sequence":"additional","affiliation":[{"name":"Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9013-7590","authenticated-orcid":false,"given":"Xiu-Xiu","family":"Zhan","sequence":"additional","affiliation":[{"name":"Research Center for Complexity Sciences, Hangzhou Normal University, Hangzhou 311121, China"},{"name":"College of Media and International Culture, Zhejiang University, Hangzhou 310027, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"20120375","DOI":"10.1098\/rsta.2012.0375","article-title":"Network Science","volume":"371","year":"2013","journal-title":"Philos. 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