In this article, a secure multiple–input multiple–output (MIMO) wireless communication system is presented and discussed. The proposed system relies on Hamiltonian graphs that are known between the transmitter (Alice) and the legitimate receiver (Bob) and not accessible for any third party intercepter. Lack of knowledge for the proper graph at the eavesdropper (Eve) is shown to substantially degrade the detection capability, where an average bit error rate (ABER) of around 0.5 is reported regardless of the considered signal-to-noise-ratio (SNR) value. The generated graph is used to construct a cycle, where the sequence of data bits to be transmitted at each time instant is converted to a decimal number and the number following this decimal number on the cycle is modulated. As well, Alice transmits a pre designed artificial noise (AN) that is know at Bob but not at Eve to enhance the secrecy rate (SR) of the communication system. It is assumed that Eve is fully aware of the communication protocol and substantial gains in terms of ABER and SR are reported.