By eXploring all seeds and computing the infection potentials for different couples of years, we obtain sharply peaked probability distributions of 71L and 71D around values that are well separated along the 7'!

Findings are however robust against changes in the choice of the threshold value, as this is induced by the peculiar bimodal shape of the probability distribution curves for the loyalty (see 81 Text).

: (i) the topological heterogeneity of each configuration of the network described by a stable probability distribution (Fig.

5A where high memory and low memory regimes are displayed) and by profiles for the probability distribution of the loyalty as in the empirical networks (Fig.

The probability distributions of several quantities measured on the different yearly networks are considerably stable over time, as e.g.

It is based on configurations from c—n to c as they are all used to build the probability distributions needed to train our approach.

Although the global energy landscape defined through the stationary probability distribution does not contain the non-gradient effect, the local pseudo energy landscape we proposed clearly visualizes this unidirectionality brought by the non-gradient force.

Consequently the system transitions to having a multipeak probability distribution , where the additional peaks do not correspond to the stable points of ODEs in the usual case.

Thus the pseudo energy landscape is only a local landscape and no longer reflects the global stationary probability distribution (See SI Text for details).