  We present our recent work on stochastic particle systems on complex
networks. As a noninteracting system we first consider the diffusive motion of
a random walker on heterogeneous complex networks. We find that the random
walker is attracted toward nodes with larger degree and that the random walk
motion is asymmetric. The asymmetry can be quantified with the random walk
centrality, the matrix formulation of which is presented. As an interacting
system, we consider the zero-range process on complex networks. We find that a
structural heterogeneity can lead to a condensation phenomenon. These studies
show that structural heterogeneity plays an important role in understanding the
properties of dynamical systems.
