{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T17:06:54Z","timestamp":1772471214886,"version":"3.50.1"},"reference-count":31,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,5,22]],"date-time":"2024-05-22T00:00:00Z","timestamp":1716336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62276272"],"award-info":[{"award-number":["62276272"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Science and Technology Innovation Program of Hunan Province","award":["2021RC3076"],"award-info":[{"award-number":["2021RC3076"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,5,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Identifying important nodes is of great significance to improving the stability and security of heterogeneous combat networks. Due to the heterogeneity of nodes and the diversity of connections, heterogeneous combat networks usually are multi-layered. In order to model the combat network more accurately and identify important nodes, this paper proposes a new important nodes identification method in multi-layer heterogeneous combat network (MHCN). This method takes into account not only the topological information between nodes, but also the meta-paths formed by node interactions and the closeness of their associations. Furthermore, it considers the uncertainty of the command and control (C2) structure within MHCN. Specifically, first, tensor representation of MHCN is proposed to represent the intra-layer network and inter-layer network between nodes. Then, meta-path and its calculation method are proposed to capture interaction information between nodes. Next, intra-layer degree centrality, meta-path centrality, combined importance of node and C2 structure entropy are proposed to identify important nodes in MHCN, which can use the interaction characteristics of intra-layer and inter-layer to measure node importance in MHCNs with different C2 structures. Finally, experiments are carried out on real combat network case to verify the effectiveness and practicality of the proposed method. The results provide useful insights for operational guidance and the design of C2 structure.<\/jats:p>","DOI":"10.1093\/comnet\/cnae021","type":"journal-article","created":{"date-parts":[[2024,6,6]],"date-time":"2024-06-06T09:37:40Z","timestamp":1717666660000},"source":"Crossref","is-referenced-by-count":3,"title":["A new important nodes identification method in multi-layer heterogeneous combat network with meta-path centrality"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4018-6693","authenticated-orcid":false,"given":"Lijian","family":"Sun","sequence":"first","affiliation":[{"name":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology , Changsha 410073, China"}]},{"given":"Yun","family":"Zhou","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology , Changsha 410073, China"}]},{"given":"Cheng","family":"Zhu","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology , Changsha 410073, China"}]},{"given":"Weiming","family":"Zhang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Information Systems Engineering, National University of Defense Technology , Changsha 410073, China"}]}],"member":"286","published-online":{"date-parts":[[2024,6,5]]},"reference":[{"key":"2024060608290082100_cnae021-B1","first-page":"0","article-title":"Dynamic identification of important nodes in complex networks by considering local and global characteristics","volume":"12","author":"Cao","year":"2024","journal-title":"J. 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