I was solving the following problem from "A First Course in Network Science" by Menczer, Fortunato & Davis. (p110, Problem 1.25)
Netflix keeps data on customer preferences using a big bipartite network connecting users to titles they have watched and/or rated. Netflix’s movie library contains approximately 100,000 titles if you count streaming and DVD-by-mail. In the fourth quarter of 2013, Netflix reported having about 33 million users. Assume the average user’s degree in this network is 1000. Approximately how many links are in this network?
My attempt Let $m=$ # of edges and $n=$# of nodes $=33\times 10^6$. The average degree of the undirected graph is $\frac{2m}{n}$. Therefore we obtain $\frac{2m}{n} = 1000$. Thus, we obtain $m = 500\times n = 500\times 33\times 10^6 = 1.65\times 10^{10}$.
The Solution from Solution Manual(Found here)
Let us use the subscripts $u$ and $m$ for users and movies, respectively. $L = N_{u}\langle k_u\rangle =33\times 10^9$.
As you can see, my solution is wrong. I am not sure what went wrong with my calculation. My guess is that we are supposed to think that the graph is directed (instead of undirected) since the average degree for a directed graph is $\frac{m}{n}$, and everything goes well with this formula. However, I am not sure how we know that we have to use a directed graph.
Average user's degree, not average degree. So the number of links is $33 \times 10^6 \times 1000 = 33 \times 10^9$.