{"id":152808,"date":"2005-02-01T00:00:00","date_gmt":"2005-02-01T00:00:00","guid":{"rendered":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/msr-research-item\/on-the-connectivity-and-diameter-of-small-world-networks\/"},"modified":"2018-10-16T20:17:03","modified_gmt":"2018-10-17T03:17:03","slug":"on-the-connectivity-and-diameter-of-small-world-networks","status":"publish","type":"msr-research-item","link":"https:\/\/cm-edgetun.pages.dev\/en-us\/research\/publication\/on-the-connectivity-and-diameter-of-small-world-networks\/","title":{"rendered":"On the connectivity and diameter of small-world networks"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We consider two different models of small-world graphs on nodes whose locations are modelled by a stochastic point process. In the first model, each node is connected to a fixed number of its nearest neighbours, while in the second, it is connected to all nodes located within some fixed distance. In both models, nodes are additionally connected via shortcuts to other nodes chosen uniformly at random. We obtain sufficient conditions for connectivity in the first model, and necessary conditions in the second. Thereby, we show that connectivity is achieved at a smaller value of total degree (nearest neighbours + shortcuts) in the first model. We also obtain bounds on the diameter of the graph in this model.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider two different models of small-world graphs on nodes whose locations are modelled by a stochastic point process. In the first model, each node is connected to a fixed number of its nearest neighbours, while in the second, it is connected to all nodes located within some fixed distance. In both models, nodes are [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2005-14","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"A. J. 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