{"paper":{"title":"On the Capacity of Fractal Wireless Networks With Direct Social Interactions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Honggang Zhang, Rongpeng Li, Ying Chen, Zhifeng Zhao","submitted_at":"2017-05-27T01:33:30Z","abstract_excerpt":"The capacity of a fractal wireless network with direct social interactions is studied in this paper. Specifically, we mathematically formulate the self-similarity of a fractal wireless network by a power-law degree distribution $ P(k) $, and we capture the connection feature between two nodes with degree $ k_{1} $ and $ k_{2} $ by a joint probability distribution $ P(k_{1},k_{2}) $. It is proved that if the source node communicates with one of its direct contacts randomly, the maximum capacity is consistent with the classical result $ \\Theta\\left(\\frac{1}{\\sqrt{n\\log n}}\\right) $ achieved by K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09751","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"}