Full connectivity: corners, edges and faces

Justin P Coon, Carl P. Dettmann, Orestis Georgiou

Research output: Contribution to journalArticle (Academic Journal)peer-review

43 Citations (Scopus)


We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.

Original languageEnglish
Pages (from-to)758-778
Number of pages21
JournalJournal of Statistical Physics
Issue number4
Publication statusPublished - Jun 2012

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