P. Erd?s and A. Rényi, On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of, Sciences, Ser. A, vol.5, issue.1, pp.17-60, 1960.

B. Bollobás, Random Graphs, 2001.

N. Alon and J. H. Spencer, The probabilistic method, 2004.

V. M. Preciado and A. Jadbabaie, Spectral analysis of virus spreading in random geometric networks, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp.4802-4807, 2009.

M. Haenggi, J. G. Andrews, F. Baccelli, O. Dousse, and M. Franceschetti, Stochastic geometry and random graphs for the analysis and design of wireless networks, IEEE Journal on Selected Areas in Communications, vol.27, issue.7, pp.1029-1046, 2009.

G. J. Pottie and W. J. Kaiser, Wireless integrated network sensors, Communications of the ACM, vol.43, issue.5, pp.51-58, 2000.

M. Nekovee, Worm epidemics in wireless ad hoc networks, New Journal of Physics, vol.9, issue.6, p.189, 2007.

H. Xiao and E. M. Yeh, Cascading link failure in the power grid: A percolation-based analysis, 2011 IEEE International Conference on Communications Workshops (ICC), pp.1-6, 2011.

D. J. Higham, M. Rasajski, and N. Przulj, Fitting a geometric graph to a proteinprotein interaction network, Bioinformatics, vol.24, issue.8, pp.1093-1099, 2008.

E. Arias-castro, S. Bubeck, and G. Lugosi, Detecting positive correlations in a multivariate sample, Bernoulli, vol.21, issue.1, pp.209-241, 2015.

M. Penrose, Random geometric graphs, vol.5, 2003.

M. D. Penrose, On k-connectivity for a geometric random graph, Random Structures & Algorithms, vol.15, issue.2, pp.1098-2418, 1999.

M. J. Appel and R. P. Russo, The connectivity of a graph on uniform points on, Statistics & Probability Letters, vol.60, issue.4, pp.351-357, 2002.

C. Mcdiarmid, Random channel assignment in the plane, Random Structures & Algorithms, vol.22, issue.2, pp.187-212, 2003.

T. Müller, Two-point concentration in random geometric graphs. Combinatorica, vol.28, p.529, 2008.

C. Mcdiarmid and T. Müller, On the chromatic number of random geometric graphs, Combinatorica, vol.31, issue.4, pp.423-488, 2011.

L. Devroye, A. György, G. Lugosi, and F. Udina, High-dimensional random geometric graphs and their clique number, Electronic Journal of Probability, vol.16, pp.2481-2508, 2011.

S. Bubeck, J. Ding, R. Eldan, and M. Z. Rácz, Testing for high-dimensional geometry in random graphs, Random Structures and Algorithms, vol.49, issue.3, pp.503-532, 2016.

Y. Lee and W. C. Kim, Concise formulas for the surface area of the intersection of two hyperspherical caps, KAIST Technical Report, 2014.

A. Brieden, P. Gritzmann, R. Kannan, V. Klee, L. Lovász et al., Deterministic and randomized polynomial-time approximation of radii. Mathematika, vol.48, pp.63-105, 2001.