{"paper":{"title":"Degree heterogeneity in spatial networks with total cost constraint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SI","stat.CO"],"primary_cat":"physics.soc-ph","authors_text":"An Zeng, Weiping Liu, Yanbo Zhou","submitted_at":"2011-12-01T16:58:30Z","abstract_excerpt":"Recently, In [Phys. Rev. Lett. 104, 018701 (2010)] the authors studied a spatial network which is constructed from a regular lattice by adding long-range edges (shortcuts) with probability $P_{ij}\\sim r_{ij}^{-\\alpha}$, where $r_{ij}$ is the Manhattan length of the long-range edges. The total length of the additional edges is subject to a cost constraint ($\\sum r=C$). These networks have fixed optimal exponent $\\alpha$ for transportation (measured by the average shortest-path length). However, we observe that the degree in such spatial networks is homogenously distributed, which is far differe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0241","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"}