(color online) Topology-induced limits of reconstructibility.

Reconstructing interaction networks from correlation thresholding may or may not yield correct connectivity pattern. (a)-(d) Successful reconstruction of a network (N = 15, average degree , γ = 1, α = 2, A_ij ∈ {0, 1} for absent and present interactions, resp.). (e)-(h) Reconstruction of statistically similar network is unsuccessful for any threshold. (a,e) Adjacency matrix of original network (black indicated directed interaction, gray undirected network aimed for). (b,f) Dynamics of the units yielding (c,g) correlation matrices. Thresholding yields (d) correct or (h) incorrect reconstruction, depending on the exact topology.