Mapping Systemic Risk: Critical Degree and Failures Distribution in Financial Networks
Fig 3
Mean number of failures as a function of mean degree z, as estimated analytically (circles) and as obtained numerically (dots), for ER networks (Fig 3a) and BA networks (Fig 3b).
The dashed line indicates the value of the critical degree k*. The discrepancy between the empirical and theoretical values at low z is due to the contribution of second neighbors, neglected in our approximation.