Mapping systemic risk: critical degree and failures distribution in financial networks Supplementary Information

We specifically analyzed Cayley trees with degree k ∈ {2, · · · 6}. For each link (i, j), the weight of a loan lij was drawn uniformly in [1 − ε, 1 + ε]. We analyzed 4 values of ε, from 0.1 to 0.4, in addition to ε = 0. This was done for 102 networks for each degree k and perturbation ε, and the resulting number of failures was measured. Figure A shows the results for R = 1.02, r = 1.01, f = 50% and for two values of Λ, namely Λ = 1% (left) and Λ = 3% (right), for which (k∗(1), k∗(2)) = (16, 3) and (k∗(1), k∗(2)) = (10, 2) respectively.