Anonymity systems are designed in a way that hides the level of communication between senders and receivers of a message, and the goal of an attacker is to find that communication pattern. It is usually very difficult to completely de-anonymize a system if it presents a black box, in which case only a global adversary can observe all messages going in and out of the system and, based on some attack, can infer the feasibility of messages being sent and received by users. This thesis presents a method to calculate the amount of anonymity present in a system after a global adversary has conducted an attack. The base model considered in this thesis considers a black box system, which allows multiple senders to send multiple input messages and multiple receivers to receive multiple output messages. A couple of approaches taken by previous researches have been analyzed and compared to the method given in this thesis, which shows that one of the methods does not consider an attack, while the other method does not cover the full spectrum of the attack plane.