English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We review mathematically tractable models for connected networks on randompoints in the plane, emphasizing the class of proximity graphs which deservesto be better known to applied probabilists and statisticians. We introduce andmotivate a particular statistic $R$ measuring shortness of routes in a network.We illustrate, via Monte Carlo in part, the trade-off between normalizednetwork length and $R$ in a one-parameter family of proximity graphs. How closethis family comes to the optimal trade-off over all possible networks remainsan intriguing open question. The paper is a write-up of a talk developed by thefirst author during 2007--2009.

Connected Spatial Networks over Random Points and a Route-Length Statistic