Anonymous Communication Network

1. what does the term anonymous communication stand for ?
2. Graphical presentation of the network problem
3. Chaum's solution
4. Is Chaum Solution Right ?(Not really)
5. The idea for our solution
6. Problems in the idea are being answered
7. what else can you find in this site ?

An external viewer will be able to easily notice when I'm sending a message and then by controlling the communication lines and using other dummy agents to find out who I'm sending to.
One idea was given by Chaum, the idea was to confuse the external viewer("the opponent") by sometimes storing the messages in one vertex(called a mix) and then distributing them in a manner that no one can trace their origin before they reached the mix. In addition, the mix also changes the message external properties, such as size.
Identifying the original message after this change, between all other messages sent (by the mix) at the same time becomes difficult. 
An external viewer cannot trace the message going thru the mix because of the distribution and the difficulty to identify what the original message was. 

Chaum gave no strong mathematical base for the assumption that anonymity is acquired. 
And indeed there is a way to trace the messages even going thru a mix!
If we use dummy agents which send messages to the mix, we get, assuming this is a communication network (meaning all messages get to their recipients), that the message that goes out off the mix and doesn't belong to any of the dummy agents (can be easily checked because dummy agents know were their messages is sent to) belongs to the real agent that uses the mix. Using this way we discover the sender and recipient, therefore, anonymity is not achieved!