Fig. 15From: Measuring Edge Importance: A Quantitative Analysis of the Stochastic Shielding Approximation for Random Processes on GraphsEdge importance distribution for graded measurement vector M. The effect of neglecting the fluctuations associated with the k th edge in an Erdös–Rényi network with n=50 nodes and edge probability p=0.5, as a function of the difference in measurement M at the two ends of the edge, M ⊺ ζ k . In this example, the components of M were assigned from the uniform distribution on [0,1], independently of the presence or absence of edges in the graph. Left: Rank order plot of edge importance R k . Compare to Fig. 7; note the absence of a clear gap distinguishing “important” from “unimportant” edges. Right: Horizontal axis, x=| M ⊺ ζ k |. Vertical axis, R k . The superimposed curve shows the quadratic y≈ x 2 /n, for n=50Back to article page