FIG. 14: Why the hubs may not be good spreaders. The probability distribution P ( M | i ) of the infected percentage for the contact network of inpatients, when the epidemic starts at two of the origin hubs in Fig. 1 i = A,B with the same degree ( k = 96), but different k$_{S}$ values ( k$_{S}$ = 63 and k$_{S}$ = 26, respectively). In each histogram, we use 1000 random realizations of the simulation, starting an SIR epidemic from the same given origin i . Despite the fact that the two origins of the epidemic spreading have the same degree, the two histograms present a radically different character. In one case (red histogram), the hub infects up to 30% of the population, while most of the spreading attempts from the other hub (yellow histogram) practically cannot propagate the infection at all. The importance of the organization of the network is highlighted when we randomly rewire the network (preserving the same degree for all nodes). In this case both distributions P ( M | A ) and P ( M | B ) coincide and both hubs contribute equally to spreading. Notice also that spreading in the rewired network extends over a much larger size of the population. “endemic” state at which exactly as many infectious individuals become susceptible as sus- 14