I'm trying to understand this claim. I see that if there are $S$ vertices, then we can identify each vertex using $\log S$ bits. Now each vertex can be connected to, let's say, $S$ other ones (is there some sort of restriction to the fan-out that I'm unaware of?). If we use an adjacency list, then for each vertex, we wold need to store up to $S \log S$ bits. Doesn't this lead to $S^2 \log S$ bits, since we need a list for each vertex? And where does the $9$ come from?