The Evolution of Systems With Weight Distribution

Here we consider digraphs and weights assigned to their vertices. When a vertex inherits the average weight of its in-neighbors, we may study the graph dynamics. One of the physical examples here is a system of heated bodies. We will see that in the case of regular graphs, the total weight of our systems is invariant. This implies the existence of special points whose weight doesn't increase (decrease). Also, we'll show that acyclic digraphs reach the static equilibrium.