I have two graphs that I've derived from an empirical data set and I suspect that they're topologically equivalent. It seems much easier to show that these graphs are not equivalent than to show that they are. For example, I've used persistent homology, but have been unable to show that they weren't equivalent. Are there any methods/techniques for this?
Further, I would be happy to know whether or not the graphs are approximately topologically equivalent. Are there any methods/techniques for this?