Fig. 15

Edge 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, $M^{⊺}{\zeta }_k$. 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, $x=|M^{⊺}{\zeta }_k|$. Vertical axis, $R_k$. The superimposed curve shows the quadratic $y\approx x^2/n$, for $n=50$