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We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.

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A study of nonlinear electromagnetic waves in a general multicomponent plasma is undertaken. Starting from an exact solution of MaxwellÏs equations and the relativistic equation of motion for the plasma species, a nonlinear dispersion relation is derived for circularly polarised electromagnetic waves that propagate along the magnetic Ðeld. New nonlinear waves are produced by Ðnite amplitude e †ects and the relativistic nature of the par-ticlesÏ motion. To illustrate the character of these waves some particular examples of two and three species plasmas are discussed in detail.

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