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the number of nodes that we consider in the comparison. By definition, M$_{eff}$ ( p ) ≥ M$_{k}$$_{S}$ ( p ), and the equality is only reached if Υ$_{eff}$( p ) = Υ$_{k}$$_{S}$( p ). We assess the imprecision of k -shell identification by calculating the ratio between M$_{eff}$ ( p ) and M$_{k}$$_{S}$ ( p ): 

Similarly, we can define ϵ$_{k}$ ( p ) and ϵ$_{C}$$_{B}$ ( p ): 

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A value for ϵ close to 0 denotes a very efficient process, since the nodes that are chosen are practically those that contribute most to epidemics. In all cases, the k$_{S}$ method yields a 

