{"paper":{"title":"Structure Entropy and Resistor Graphs","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.DM","authors_text":"Angsheng Li, Yicheng Pan","submitted_at":"2018-01-09T06:48:51Z","abstract_excerpt":"We propose the notion of {\\it resistance of a graph} as an accompanying notion of the structure entropy to measure the force of the graph to resist cascading failure of strategic virus attacks. We show that for any connected network $G$, the resistance of $G$ is $\\mathcal{R}(G)=\\mathcal{H}^1(G)-\\mathcal{H}^2(G)$, where $\\mathcal{H}^1(G)$ and $\\mathcal{H}^2(G)$ are the one- and two-dimensional structure entropy of $G$, respectively. According to this, we define the notion of {\\it security index of a graph} to be the normalized resistance, that is, $\\theta (G)=\\frac{\\mathcal{R}(G)}{\\mathcal{H}^1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.03404","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"}