In this work, we formulate and study a data dissemination problem, which can be viewed as a generalization of the index coding problem and of the data exchange problem to networks with an arbitrary topology. We define $r$-solvable networks, in which data dissemination can be achieved in $r>0$ communications rounds. We show that the optimum number of transmissions for any one-round communications scheme is given by the minimum rank of a certain constrained family of matrices. For general r-solvable networks, we derive an upper bound on the minimum number of transmissions in any scheme with $\geq r$ rounds. We experimentally compare the obtained upper bound to a simple lower bound.