{"paper":{"title":"Scale-free Loopy Structure is Resistant to Noise in Consensus Dynamics in Complex Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI"],"primary_cat":"cs.SY","authors_text":"Stacy Patterson, Yuhao Yi, Zhongzhi Zhang","submitted_at":"2018-01-02T02:51:33Z","abstract_excerpt":"The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution and a constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices are subject to white noise. We focus on the coherence of networks characterized in terms of the $H_2$-norm, which quantifies how closely agents track the consensus value. We first provide a lower bound of coherence of a network in terms of its average degree, which is independent of the network order. We then study the coherence of some sparse, scale-fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00535","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"}