{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,9]],"date-time":"2026-09-09T05:07:10Z","timestamp":1788930430347,"version":"build-2803163510"},"reference-count":34,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T00:00:00Z","timestamp":1788307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The identification of influential nodes in directed networks is fundamental to diffusion analysis, network robustness assessment, and information recommendation. Owing to the asymmetry introduced by directed edges, conventional centrality methods often struggle to jointly characterize the local spreading range, higher-order diffusion potential, and structural bridging roles. To address this issue, this paper proposes KSGR for influential node identification in directed networks. Under the convention that a node can influence its in-neighbors, KSGR integrates the reverse local reachability, reverse diffusion efficiency, hierarchical asymmetry, directed reverse k-shell, reverse structural gravity, bridging capability, and structural diversity enhancement. A lightweight network-profiling mechanism based on the network size, reciprocity, LWCC ratio, and SCC ratio is further used to select structural enhancement branches for different network profiles. Experiments on six real-world directed networks compare KSGR with PageRank, LeaderRank, ClusterRank, In-degree, Adjacency Entropy, BII, and NEM. Under the adopted reverse-edge propagation convention and SI settings, KSGR achieves the highest average normalized spreading AUC and final infection scale in the Top-10 seed experiments among the selected methods. Supplementary Top-5 and Top-20 experiments further indicate that the ranking can be applied to different seed-set sizes. Kendall correlation analysis shows that KSGR produces rankings distinct from traditional centrality and random-walk-based methods. LWCC node-removal experiments provide evidence that highly ranked KSGR nodes influence the weakly connected backbone of the tested networks. Parameter sensitivity and threshold robustness analyses demonstrate that KSGR maintains stable spreading performance under different enhancement settings and moderate perturbations of adaptive branch-selection thresholds.<\/jats:p>","DOI":"10.3390\/e28090981","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T15:39:47Z","timestamp":1788363587000},"page":"981","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["KSGR: An Influential Node Identification Algorithm for Directed Networks Integrating Reverse Reachability and Structural Enhancement Mechanisms"],"prefix":"10.3390","volume":"28","author":[{"given":"Zi-Yue","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo-Lin","family":"Hu","sequence":"additional","affiliation":[{"name":"International School, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"107365","DOI":"10.1016\/j.knosys.2021.107365","article-title":"Identifying super-spreaders in information\u2013epidemic coevolving dynamics on multiplex networks","volume":"229","author":"Zeng","year":"2021","journal-title":"Knowl.-Based Syst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"104198","DOI":"10.1016\/j.engappai.2021.104198","article-title":"Soft rumor control in social networks: Modeling and analysis","volume":"100","author":"Askarizadeh","year":"2021","journal-title":"Eng. 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