FIG. 7: Cross-plots of M$_{i}$ as a function of T$_{i}$ , and M$_{i}$ as a function of E$_{i}$ (inset) for a) email, b) hospital inpatients, c) actor network and d) RL Internet. Every point denotes the corresponding quantities for a given node, and the color denotes the k -shell index of this node. The k$_{S}$ values are aggregated and highlighted with red (large k$_{S}$ regime), green (intermediate k$_{S}$ regime) and blue (low k$_{S}$ values) colors, respectively. A high level of correlation between M$_{i}$ and E$_{i}$ indicates that the most efficient spreaders (as measured by M$_{i}$ ) are the most likely to be infected during an epidemic outbreak originating at random inpatient in the network. On the other hand, the anti-correlation between M$_{i}$ and T$_{i}$ indicates that the most efficient spreaders are typically infected earlier than other nodes during an epidemic outbreak. assess the merit of using k -shell decomposition to identify the most efficient SIR spreaders one needs to compare the two sets Υ$_{eff}$( p ) and Υ$_{k}$$_{S}$( p ). In order to consider individual M$_{i}$ values, we calculate the average M$_{eff}$ ( p ) and M$_{k}$$_{S}$ ( p ) values for the sets Υ$_{eff}$( p ) and Υ$_{k}$$_{S}$( p ) respectively: M$_{k}$$_{S}$ ( p ) ≡ ∑ i ∈ Υ$_{k}$$_{S}$ ( p $_{)}$M$_{i}$ /Np and M$_{eff}$ ( p ) ≡ ∑ i ∈ Υ$_{eff}$ ( p $_{)}$M$_{i}$ /Np , where Np is 6