Consider a network with N nodes. Assume that each node is connected to every other node. At time $0$ a cat resides on node N and a mouse resides on node $1.$ During one time unit the cat chooses a random node from the remaining N $1$ nodes and moves to it$.$ The mouse moves in the same way independently of the cat. If the cat and the mouse occupy the same node at any time, the cat promptly eats the mouse. Now let Xn $=0$ or $1,$ if the mouse is dead or alive respectively, at time n$.$ Model $\{$Xn$,$ n $0\}$ as a DTMC$.$