The Inverse Contagion Problem (ICP) vs.

We have observed the distribution of false link difficulty for various network types, estimated it theoretically and confronted it (successfully) with the numerical simulations. Based on it, we estimated analytically the convergence of the ICP solution (as a function of the number of contagion histories observed), and found it to be in perfect agreement with simulation results. Finally, the most important insight we obtained is that SICP and WICP are have quite different properties: if one in interested only in the operational aspect of predicting how contagion will spread, the links which are most difficult to decide about are the least influential on contagion dynamics. In other words, the parts of the network which are harder to reconstruct are also least important for predicting the contagion dynamics, up to the point where a (large) constant number of false links in the network (i.e. non-convergence of the network reconstruction procedure) implies a zero rate of the node contagion prediction errors (perfect convergence of the WICP). Thus, the contagion prediction problem (WICP) difficulty is very different from the network reconstruction problem (SICP), in as far as links which are difficult to reconstruct are quite harmless in terms of contagion prediction capability (WICP).