Cosmological simulations play an important role in testing cosmological structure formation models against observations. Identification of virialized peaks, or halos, in simulations, and the characterization of their properties is of critical importance as most of the observational information comes from such peaks. The friends-of-friends algorithm (hereafter, FOF) is a percolation algorithm which is routinely used to identify bound dark matter halos from N-body simulations. We present a detailed analysis of the boundary of halos and the corresponding overdensity selected by the FOF algorithm using Monte Carlo realizations of dark matter halos. We present an analytical interpretation of the results based on percolation theory. We show that the overdensity of FOF halos depends upon the linking length parameter (b), the concentration parameter of the halo, and also on the numerical resolution with which the halo was sampled. Our analytical predictions of overdensity are in excellent agreement with overdensities of real halos measured from N-body simulations. We discuss the implications of our results for the determination of the halo mass function from simulations and comment on its universal behavior.
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