{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T10:48:42Z","timestamp":1761648522582,"version":"build-2065373602"},"reference-count":62,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T00:00:00Z","timestamp":1520380800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["71371073"],"award-info":[{"award-number":["71371073"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Pujiang Program of China","award":["13PJC025"],"award-info":[{"award-number":["13PJC025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We analyze the dimension of a financial correlation-based network and apply our analysis to characterize the complexity of the network. First, we generalize the volume-based dimension and find that it is well defined by the correlation-based network. Second, we establish the relationship between the R\u00e9nyi index and the volume-based dimension. Third, we analyze the meaning of the dimensions sequence, which characterizes the level of departure from the comparison benchmark based on the randomized time series. Finally, we use real stock market data from three countries for empirical analysis. In some cases, our proposed analysis method can more accurately capture the structural differences of networks than the power law index commonly used in previous studies.<\/jats:p>","DOI":"10.3390\/e20030177","type":"journal-article","created":{"date-parts":[[2018,3,7]],"date-time":"2018-03-07T12:55:23Z","timestamp":1520427323000},"page":"177","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["Relationship between Entropy and Dimension of Financial Correlation-Based Network"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7790-0803","authenticated-orcid":false,"given":"Chun-xiao","family":"Nie","sequence":"first","affiliation":[{"name":"Department of Finance, School of Business, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fu-tie","family":"Song","sequence":"additional","affiliation":[{"name":"Department of Finance, School of Business, East China University of Science and Technology, Shanghai 200237, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,3,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.physrep.2005.10.009","article-title":"Complex networks: Structure and dynamics","volume":"424","author":"Boccaletti","year":"2006","journal-title":"Phys. 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