Good evening, I want to show that a random walk on a graph is recurrent, the graph is a network of nodes which connect together to make a N by M square grid, such as this, my first thought was to somehow get an expression for

$mathbb{P}[text{on node} n text{after} i text{jumps}]$,

then express

$mathbb{P}[text{on node} 0 text{after} i text{jumps}|text{on node} 0 text{at} i=1]$

then let $itoinfty$ and hope it $=1$.

Does this sound like the right approach, any pointers?