graph similarity having multiple edges between two nodes

Question

There are many theories about calculating of graph similarity such as vertex edge overlap, jacard, co-sine, edit distance, signature similarity, lambda distance, deltacon so on. These things are based on single edge of the graph. But there are many graphs having multiple edges in real world.

Given similar two graphs like above, how could we calculate graph similarity? Using previous graph similarity, there are only 2-dimension vector and the entry is just scalar that is number, but in multiple edge's graph, the entry should be tuple. Because there are one more actions between nodes. For the previous method, it could be called who-knows-whom schem, but latter graph, it could be said who-knows-whom*-how*. I think the previous mothods could be used for the multiple edge's graph easily, so there aren't logic or methods about it. Thanks in advance!

Answer 1

There is not "the" way yo compute graph similarity.

Depending on your data and problem, very different approaches may be good. In many cases, simply merging the two edges into one makes perfect sense. For example, if I have two roads of capacity x and y to go from A to B - for many analyses this is comparable to having just one rode, with the combined capacity.