# Math Help - Graph Theory Puzzle

1. ## Graph Theory Puzzle

Let $G$ be a graph with average degree $d$. Show that there exists a vertex $v \in V(G)$ such that the average degree of neighbours of $v$ is at least $d$.

2. Does anyone have any ideas? Incidentally, there does not necessarily have to exist a vertex such that the average degree of neighbours is at most d, so I think there is at least something slightly subtle going on...