  In this paper, we consider the quantum-mechanical phase space patterns on
ordered and disordered networks. For ordered networks in which each node is
connected to its 2m nearest neighbors (m on either side), the phase space
quasi-probability of Wigner function shows various patterns. In the long time
limit, on even-numbered networks, we find an asymmetric quasi-probability
between the node and its opposite node. This asymmetry depends on the network
parameters and specific phase space positions. For disordered networks in which
each edge is rewired with probability p>0, the phase space displays regional
localization on the initial node.
