{"paper":{"title":"The energy of random signed graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuchao Li, Shujing Wang","submitted_at":"2018-12-27T13:11:13Z","abstract_excerpt":"A signed graph $\\Gamma(G)$ is a graph with a sign attached to each of its edges, where $G$ is the underlying graph of $\\Gamma(G)$. The energy of a signed graph $\\Gamma(G)$ is the sum of the absolute values of the eigenvalues of the adjacency matrix $A(\\Gamma(G))$ of $\\Gamma(G)$. The random signed graph model $\\mathcal{G}_n(p, q)$ is defined as follows: Let $p, q \\ge 0$ be fixed, $0 \\le p+q \\le 1$. Given a set of $n$ vertices, between each pair of distinct vertices there is either a positive edge with probability $p$ or a negative edge with probability $q$, or else there is no edge with probabi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.11865","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}