can you check my soultion?
Task:In graph G every two vertices have odd number of common neighbors. Prove that every vertex has even degree.
My thinking. I choose arbitrary vertex $v$ and build subgraph, which contain this vertex and all his neighbors. Every neighbor has even degree (odd common neighbors plus chosen vertex). But in every graph (subgraph) sum of degrees is even,so vertex $v$ has to have even degree. That ends the proof. Is it correct?