  Quantum mutual information (QMI) not only displays the mutual information in
the system but also demonstrates some quantum correlation beyond entanglement.
We explore here the two alternatives of multipartite quantum mutual information
(MQMI) based on the von Neumann entropy according to the framework of the
complete measure of multi-particle quantum system. We show that these two MQMI
are complete, monogamous on pure states, and one of them is not only completely
monogamous but also tightly complete monogamous while another one is not.
Moreover, we present another two MQMI by replacing the von Neumann entropy with
the Tasllis $q$-entropy from the former two ones. It is proved that one of them
displays some degree of ``completeness'' as a measure of multi-particle quantum
system, but the other one is not even non-negative and thus it can not be a
alternative of MQMI. We also discuss the triangle relation for these three
alternatives of MQMI. It is shown that the triangle inequalities hold for the
former two MQMI as that of entanglement measure but the later one fails. By
comparison, we found that the von Neumann entropy is better than other versions
of entropy as desired when we characterize the quantum correlation in
multi-particle system.
