0. (Graph random walk) Let G=(V, E) be a finite simple graph with a set of vertices V and a set of (undirected) edges E. Let A = {a(x, y)}x,yes be the adjacency matrix of G, that is, i, if there is an edge in the graph between the vertices x and y; a(x, y) if there is no such edge. The degree deg(x) of a vertex x is the number of edges connected to the vertex. So deg(x) = {yev a(x, y). The simple random walk on the graph G is the Markov chain with the state space S = V and transition matrix P, given by a(x, y) p(x, y) = deg(x) Show that 7(x) = cdeg(x) is a stationary distribution for a suitable choice of constant c, and determine the value of c. 0. (Graph random walk) Let G=(V, E) be a finite simple graph with a set of vertices V and a set of (undirected) edges E. Let A = {a(x, y)}x,yes be the adjacency matrix of G, that is, i, if there is an edge in the graph between the vertices x and y; a(x, y) if there is no such edge. The degree deg(x) of a vertex x is the number of edges connected to the vertex. So deg(x) = {yev a(x, y). The simple random walk on the graph G is the Markov chain with the state space S = V and transition matrix P, given by a(x, y) p(x, y) = deg(x) Show that 7(x) = cdeg(x) is a stationary distribution for a suitable choice of constant c, and determine the value of c