I have two graphs that represent the same traffic network with the same exact vertices and edges, the only difference between them is the weights on the edges of the graph that represent the travel time between two vertices. Is there a good way of comparing the two graphs and output a number as to how similar they are?
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$\begingroup$ Do you want to measure how similarly fast they allow a single traveler to go between any two vertices? Do you have an added concern about maximal flows of many travelers? $\endgroup$ – Claude Chaunier May 7 at 11:10

$\begingroup$ Do you assume directed or undirected edges? $\endgroup$ – Manfred Weis May 7 at 12:06

$\begingroup$ Assuming directed edges. Suppose the weights on one of the graphs is gathered from real world data and the other one is gathered from my simulated work, I want to be able to compare how "far off" my simulated work is from the truth. No constraints on maximal flow. $\endgroup$ – Dia Vulpecula May 7 at 20:44