$($a$)$ A particle performs a random walk on the vertex set of an undirected connected

graph G$,$ which for simplicity we assume to have neither loops $($vertices connected to

themselves$)$ nor multiple edges $($two or more edges between the same vertices.$)$ At

each stage it moves to a neighbour of its current position, each such neighbour being

chosen with equal probability. If G has $\backslash$eta $(<\backslash$infty $)$ edges, show that the stationary

distribution is given by $\backslash$pi i $=$ di$/(2\backslash$eta $),$ where di is the degree of vertex i $($the number

of edges coming out of it$.)$