Symmetric motifs in random geometric graphs

Carl Dettmann*, Georgie Knight

*Corresponding author for this work

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

5 Citations (Scopus)
175 Downloads (Pure)


We study symmetric motifs in random geometric graphs. Symmetric motifs are subsets of nodes which have the same adjacencies. These subgraphs are particularly prevalent in random geometric graphs and appear in the Laplacian and adjacency spectrum as sharp, distinct peaks, a feature often found in real-world networks. We look at the probabilities of their appearance and compare these across parameter space and dimension. We then use the Chen-Stein method to derive the minimum separation distance in random geometric graphs which we apply to study symmetric motifs in both the intensive and thermodynamic limits. In the thermodynamic limit, the probability that the closest nodes are symmetric approaches one, while in the intensive limit this probability depends upon the dimension.

Original languageEnglish
Article numbercnx022
Pages (from-to)95-105
Number of pages11
JournalJournal of Complex Networks
Issue number1
Early online date26 Jul 2017
Publication statusPublished - 1 Feb 2018


  • Random geometric graph
  • Spectrum
  • Motif
  • Chen-Stein method


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