Lectures on random geometric graphs

by Mathew Penrose. Pages 67-101 of

Random Graphs, Geometry and Asymptotic Structure

By M. Krivelevich, K. Panagiotou, M. Penrose and C. McDiarmid. Edited by N. Fountoulakis and D. Hefetz. Cambridge University Press, May 2016

These lecture notes, based on a mini-course delivered in 2013, complement my more comprehensive monograph Random Geometric Graphs. The presentation here is selective, and somewhat simplified by comparison with the latter work. The material on Hamiltonian paths, and the exercises, do not feature in that work. For more information on the volume as a whole, see the publisher's description.


Introduction; Edge counts; Edge counts: normal approximation; the maximum degree; a sufficient condition for connectivity; connectivity and Hamiltonicity; solutions to exercises.

Link to author's main page

Last update to this page: 08 June 2016.