Fig. 7

Rank order of edge importance for the Erdös–Rényi ensemble. Edge importance values $R_k$ plotted in descending order for the process on an Erdös–Rényi random graph with 50 nodes, edge probability 0.5, and measurement functional M such that half the nodes are labeled 1 and the other half are 0. There is a clear separation between the important edges (type 0–1) and unimportant edges (types 0–0 and 1–1). The cluster of important edges has a mean $R_k$ value of $1/50=0.02$ whereas the unimportant cluster lies below the line at $\sqrt{2}{n}^{-5/3}\approx 0.0021$