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You basically need the person that's paying you to stop paying you when it stops being open. You need the value they receive to evaporate when you close the graph off. Once you have the graph, you hold the value and can extract any rent you choose to.
I think you need others to have the graph and ideally many of them. If you can incentivize competitors to also serve the graph, that'd prevent any one company from successfully extorting customers.