(Rank of the Conservation of Flow Equations) Let us say that the conservation of flow equations (a) Show that if the graph is connected, the conservation of flow equations have rank N − 1, where N is...

(Rank of the Conservation of Flow Equations) Let us say that the conservation of flow equations

(a) Show that if the graph is connected, the conservation of flow equations have rank N − 1, where N is the number of nodes. Hint: Use a spanning tree of the graph.

(b) Show that the conservation of flow equations have rank N − r if the graph is the union of r disconnected subgraphs, each of which is connected by itself