{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T12:23:06Z","timestamp":1788351786807,"version":"build-2803163510"},"reference-count":51,"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>Rumor events on social media generate opposing camps whose interaction structure is not captured by spreading models or content detectors. This study describes the camp and bridging structure of three rumor events on Sina Weibo, selected from confirmed cases published by the platform\u2019s rumor-refutation channel. Each event is represented as a multilayer interaction network built from repost, comment, and mention relations. Camps are detected by modularity-based community assignment, and overlap is measured through a fractional membership distribution over communities. Three information-theoretic quantities characterize the structure. In the three events, membership entropy separates committed users from bridging users. Structure-to-stance mutual information measures the alignment between interaction communities and text stance. Cross-layer mutual information measures the consistency of camps across interaction types. A co-opetition matrix of mean edge sentiment describes cooperation within camps and competition between camps and identifies alliance structure. In the three events, membership entropy is bimodal, structure-to-stance mutual information is positive and above a permutation null, and the co-opetition matrix has positive diagonal entries. The three events show three distinct temporal patterns, namely a persistent standoff, a hardening toward a single camp after an official correction, and a reversal with an alliance between two camps. The patterns are recovered under a look-ahead-free temporal scheme. In the three events, bridging users hold higher betweenness centrality than non-bridging users. The results describe cross-camp bridging structure in three rumor cascades and connect the structure to a co-opetition reading of camp relations.<\/jats:p>","DOI":"10.3390\/e28090978","type":"journal-article","created":{"date-parts":[[2026,9,2]],"date-time":"2026-09-02T12:04:16Z","timestamp":1788350656000},"page":"978","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Co-Opetitive Bridging Structure in Rumor Cascades: A Multilayer Overlapping Community Approach with Information-Theoretic Characterization"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-1408-2644","authenticated-orcid":false,"given":"Sijia","family":"Sun","sequence":"first","affiliation":[{"name":"Zhejiang Institute of Administration, Hangzhou 311121, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]},{"given":"Tian","family":"Liu","sequence":"additional","affiliation":[{"name":"Economic Department, Capital University of Economics and Business, Beijing 100070, China"},{"name":"Leshan Institute of Administration, Leshan 614000, China"}],"role":[{"vocabulary":"crossref","role":"author"},{"role":"conceptualization","vocabulary":"credit"},{"role":"visualization","vocabulary":"credit"},{"role":"investigation","vocabulary":"credit"},{"role":"methodology","vocabulary":"credit"},{"role":"resources","vocabulary":"credit"},{"role":"supervision","vocabulary":"credit"},{"role":"project-administration","vocabulary":"credit"},{"role":"data-curation","vocabulary":"credit"},{"role":"software","vocabulary":"credit"},{"role":"validation","vocabulary":"credit"},{"role":"writing-original-draft","vocabulary":"credit"},{"role":"funding-acquisition","vocabulary":"credit"},{"role":"writing-review-editing","vocabulary":"credit"},{"role":"formal-analysis","vocabulary":"credit"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e70247","DOI":"10.1111\/risa.70247","article-title":"A Systematic Review of Controlling Rumors in Online Social Networks: Insights From Epidemiological Models","volume":"46","author":"Karmaker","year":"2026","journal-title":"Risk Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"386","DOI":"10.1016\/j.geb.2025.07.007","article-title":"A game-theoretic model of misinformation spread on social networks","volume":"153","author":"Hsu","year":"2025","journal-title":"Games Econ. 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