{"paper":{"title":"Giant component sizes in scale-free networks with power-law degrees and cutoffs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","physics.data-an"],"primary_cat":"physics.soc-ph","authors_text":"A.J.E.M. Janssen, Johan S.H. van Leeuwaarden","submitted_at":"2015-11-30T10:42:55Z","abstract_excerpt":"Scale-free networks arise from power-law degree distributions. Due to the finite size of real-world networks, the power law inevitably has a cutoff at some maximum degree $\\Delta$. We investigate the relative size of the giant component $S$ in the large-network limit. We show that $S$ as a function of $\\Delta$ increases fast when $\\Delta$ is just large enough for the giant component to exist, but increases ever more slowly when $\\Delta$ increases further. This makes that while the degree distribution converges to a pure power law when $\\Delta\\to\\infty$, $S$ approaches its limiting value at a s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.09236","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"}