I'm currently reading Lovasz's survey on random walks. He claims without proof in Proposition 2.3 that the expected time taken for a simple random walk starting at a vertex $u$ to return to $u$ is equal to $2m/d_u$, where $m$ is the number of edges in the underlying graph and $d_u$ is the degree of $u$.
Just wondering if anyone can provide a proof or some intuition behind it? Thanks.