For i and iii, the symmetry of the graph dictates that each node is the same as every other node. Clearly the equilibrium distribution is the one where each node has 1/5 of the total.
a) LetK5 be the graph with vertices {1,2,3,4,5} and edges {12,13,14,15,23,24,25,34,35,45} (so every pair of vertices are joined). Consider the random walk on K5.
i) How do you know that this has a unique equilibrium distribution?
ii) How do you know that it has a limiting distribution?
iii) Without solving any equations write down the equilibrium distribution.
thanks for any help.