In each of the graphs pictured, assume that each arrow leaving a vertex has an equal chance of being followed.

Hence if there are thee arrows leaving a vertex then there is a $\frac{1}{3}$ chance of each being followed.

For each of the six pictures, find the Markov transition matrix.

State if the Markov chain given by this matrix is irreducible and if the matrix is doubly stochastic.

If the Matrix is irreducible, state if it is aperiodic.

When possible $($given what you know$),$ state if each chain has a unique stationary distribution. If it is

obvious that the system does not possess a unique stationary distribution, please state why.

For two of the chains it is easy to state what is this unique stationary distribution. Which two and what

are the two stationary distributions?