  The study of quantum evolution on graphs for diversified topologies is
beneficial to modeling various realistic systems. A systematic method, the
dimerized decomposition, is proposed to analyze the dynamics on an arbitrary
network. By introducing global "flows" among interlinked dimerized subsystems,
each of which locally consists of an input and a output port, the method
provides an intuitive picture that the local properties of the subsystem are
separated from the global structure of the network. The pictorial
interpretation of quantum evolution as multiple flows through the graph allows
for the analysis of the complex network dynamics supplementary to the
conventional spectral method.
