# Rank graph edges by importance

I have a graph data structure that represents a rail network. The nodes of the network are the train stations and the edges are the connections between stations.

Running PageRank on this graph gives me a way to rank the stations by importance. But I want to rank the connections between stations, the edges of the graph, by importance.

Is there an appropriate algorithm to do this? Is there a way to reformat the graph so that I can run PageRank for edges?

• What have you tried and where did you get stuck? There's a rather standard transformation from one graph to another so that edges in one correspond to nodes in the other, and vice versa. – Raphael Apr 5 '16 at 12:01
• Are you positive that page rank is a suitable measure of importance in this application? – Raphael Apr 5 '16 at 12:02
• PageRank on nodes would mean how much they're connected to the rest of the network. What would PageRank mean on edges? – Auberon Apr 5 '16 at 14:35
• You need to define what you mean by importance before you can decide whether any particular algorithm can calculate it correctly. – reinierpost Apr 5 '16 at 14:56
• Also, are you sure your data structure is appropriate? Railway lines very often have junctions that aren't at stations. The true structure is often not that there are lines from city A to cities B and C but, rather, there's a line from A to some point X, where there is no station, and from X to B and C. This seems relevant to your notion of importance since, if the line from A to X is blocked, you can't get to B or C. – David Richerby Apr 5 '16 at 15:07