The purpose of this thesis is to illuminate several characteristics of Facebook user networks in order to model user network formation in Facebook. Based on the amount of data gathered during a seven-month period, we conclude that the user network node degree distribution in Facebook follows a Lognormal distribution, and the distribution increase in the number of fan's of Facebook's web pages follows the Weibull distribution. Also we present that the Facebook user network graph has small world characteristic. Finally, by using the distributions that modeled the Facebook user networks with the small world characteristic, this thesis proposes a new algorithm in order to simulate a Facebook user network graph and the increase in the number of Facebook's web page fans. We built the software that generates the graphs with similar static and dynamic characteristics of Facebook user networks.