PageRank algorithm for weighted graphs

Question

I have a situation like this: Assume graph G has 4 nodes and 2 edges: edge A to B with weight 0.9 and edge C to D with weight 0.1.
In PR algorithm for weighted graph, all weights of outlinks from one node are normalized so that their sum is to 1. Hence, in my example, two weights are converted to 1, then the pagerank values of B and D are equal.
I need a modified version of this algorithm such that D gets less mass (or votes) from C than B from A because edge C to D has less weight. And finally, the final value of D is less than that of B.
I don't know if there is anyone did that before. If not, could you give me some suggestion. Any help is appreciated.

This is my first question on SO. Sorry if there is any confusion.

EDIT: OK, it seems that there's no algorithm like that.
So let me restate my problem in a different way: I want to find a algorithm such that the mass (or information) is propagated from set of source nodes to all the other nodes in a graph. The amount of mass transferred through an edge depends on the weight, ie the less weight is the less mass is transferred, and vice versa.

Answer 1

Just normalize all edges. In your example, this is already the case.