Fig. 2.

Empirical evaluation of the bound in Theorem 2 on ${10}^3$ random strongly friendly graphs. For each graph, different amount of noise was added, and the ratio of successful runs of convex relaxation (Eq. 8) recorded on the vertical axis (a run was deemed successful if the ground truth isomorphism is recovered). The noise strength on the horizontal axis is normalized for each graph in such a way that the value of the bound is always 1. Observe that all runs with noise within the bound converged successfully, while those with stronger noise failed with probability increasing as the amount of noise grows.