  We show that the limiting state vector in the differential model of consensus
seeking with an arbitrary communication digraph is obtained by multiplying the
eigenprojection of the Laplacian matrix of the model by the vector of initial
states. Furthermore, the eigenprojection coincides with the stochastic matrix
of maximum out-forests of the weighted communication digraph. These statements
make the forests consensus theorem. A similar result for DeGroot's iterative
pooling model requires the Cesaro (time-average) limit in the general case. The
forests consensus theorem is useful for the analysis of consensus protocols.
