  We introduce a broad class of analytically solvable processes on networks. In
the special case, they reduce to random walk and consensus process - two most
basic processes on networks. Our class differs from previous models of
interactions (such as stochastic Ising model, cellular automata, infinite
particle system, and voter model) in several ways, two most important being:
(i) the model is analytically solvable even when the dynamical equation for
each node may be different and the network may have an arbitrary finite graph
and influence structure; and (ii) in addition, when local dynamic is described
by the same evolution equation, the model is decomposable: the equilibrium
behavior of the system can be expressed as an explicit function of network
topology and node dynamics
