A Survey of Modern Analysis on Graphs: Open Problems

Commute times/effective resistances have long been used for semi-supervised learning on graphs due to multiple appealing heuristic justifications and relative ease of computation. However, recent external work by von Luxburg and collaborators has shown that commute times/effective resistances in certain classes of random geometric graphs may converge to trivial local quantities. The extent of this phenomenon is not presently known. Given a general large graph, it would be helpful to know whether or not the output of such algorithms will exhibit this pathology.