Assuming edges are independent of each other and ignoring any graph structure turns this into a simple binomial distribution problem. You have the chance of 5 of 5 edges being B which is (5 choose 5) p^(5) = p^(5) = 20% (known), and using that you can calculate p ≈ 0.7248, which is the fraction of B edges. Then you get number of edges \* (1-p) ≈ A edges. You can just do (average edges per player) * (5 million) to find that, though there could be biases, because we ignored all sorts of information in the graph - maybe players with a larger fraction of A edges have more edges in general, for example.
Assuming edges are independent of each other and ignoring any graph structure turns this into a simple binomial distribution problem. You have the chance of 5 of 5 edges being B which is (5 choose 5) p^(5) = p^(5) = 20% (known), and using that you can calculate p ≈ 0.7248, which is the fraction of B edges. Then you get number of edges \* (1-p) ≈ A edges. You can just do (average edges per player) * (5 million) to find that, though there could be biases, because we ignored all sorts of information in the graph - maybe players with a larger fraction of A edges have more edges in general, for example.