The purpose of this paper is to model and study the effectiveness of an attack on the anonymity of Internet users by a group of collaborating eavesdroppers. The paper is based on an analysis of the Internet topology. The study is based on two methods for choosing nodes that contribute the most to the detection of as many communicating Internet users as possible. The paper proposes a new measure of anonymity level in the network, based on the linkability of the Internet users. This paper is the first to present results of a non-trivial Group Betweenness optimization strategy in large complex networks.