My question is the following:
What does "fraction" mean in the sentence: "Let us define a k x k symmetric matrix e whose element $e_{ij}$ is the fraction of all edges in a network that link vertices in community i to vertices in community j"
I have tried searching around the web, tried looking at the reference the article refers to when they describe it, but there is no explanation anywhere, so it is probably something extremely simple that I just ain't getting.
If there are $x$ edges in total in the network, and there are $y$ edges in the network that link vertices in community $i$ to vertices in community $j$, then $e_{ij} = \frac{x}{y}$.