3

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, i.e. the less weight is the less mass is transferred, and vice versa.

Arnold
  • 199
  • 7
  • 2
    Can't resist. Did you try googling for a solution? ;-) – Knoothe Mar 26 '13 at 07:38
  • I tried, but not successfully. You can put my question on personalized PR, a special case of PR, where the teleportation is to a set of nodes, not all nodes in the graph. – Arnold Mar 26 '13 at 13:10
  • Please give me some suggestion! Thank you! – Arnold Mar 28 '13 at 08:07
  • I got notified by your previous comment. Sorry can't help you there. I have no clue about pagerank, other than the fact that Google uses it (hence my attempt at humor earlier). – Knoothe Mar 29 '13 at 18:43
  • looks to me like you want to do random walks from a set of source vertices on a weighted graph. – marcorossi Mar 19 '14 at 16:26

1 Answers1

1

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

Philip
  • 5,795
  • 3
  • 33
  • 68
  • PR requires normalization all weights of outlinks of one node so that they sum to 1. How can we achieve that if we normalize all edges like you said? – Arnold Mar 26 '13 at 13:05