$2\mathrm{.}4$ Consider a completely connected network of N nodes. At time $0$ a cat resides

on node N and a mouse on node $1.$ During one time unit, the cat chooses a random

node uniformly from the remaining N $1$ nodes and moves to it$.$ The mouse moves

in a similar way, independently of the cat. If the cat and the mouse occupy the same

node, the cat promptly eats the mouse. Model this as a Markov chain.