I found this tree and found it an excellent visualisation:
Could anyone provide me with a graph that includes all common chess openings but to a lesser depth?
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If this helps, I'm developing an interactive tree graph with chess traps and openings at http://www.chesstree.net. Currently, it shows common openings, how often they are used, and their win-loss ratios. You can also search openings and save your custom openings with comments. It also has a batch of traps in it, although their presentation is yet somewhat unrefined.
Perhaps you were looking for something like this: http://www.chessfornovices.com/chessopeningsconclusion.html
If your search is still ongoing, I have a chess tree with all the openings for you. There is also printable pdf version on https://named-openings-galore.com/