Transition to reconstructibility for weak coupling.

(a) Correlation thresholding yields different estimators (shaded areas with graphs as insets) for a given topology (adjacency matrix on bottom right) depending on coupling strength and threshold. For sufficiently small coupling strength α (left of gray dashed line), there are ideal thresholds yielding perfect reconstruction (green shading). (Analytic results obtained using (3) and (5).) (b) Fraction of reconstructible networks exhibits transition to full reconstructibility at positive coupling strength α (inset) and αN (main panel), illustrated for random networks of N ∈ {16, 64, 256} units and link probability p = 0.5. Every arbitrary network exhibits such a transition individually (see text).