  We study spectra and localization properties of Euclidean random matrices.
The problem is approximately mapped onto that of a matrix defined on a random
graph. We introduce a powerful method to find the density of states and the
localization threshold. We solve numerically an exact equation for the
probability distribution function of the diagonal element of the the resolvent
matrix, with a population dynamics algorithm, and we show how this can be used
to find the localization threshold. An application of the method in the context
of the Instantaneous Normal Modes of a liquid system is given.
