14 yield comparable results for p = 2%, the k -shell strategy is consistently more accurate for 2% < p < 10% with ϵ$_{k}$$_{S}$ approximately twice lower than ϵ$_{k}$ . The C$_{B}$ identification of the most efficient spreaders is the least accurate, with ϵ$_{C}$$_{B}$ exceeding 40%. b, We visualize the CNI network as a set of concentric circles of nodes representing inpatients, each circle corresponding to a particular k -shell. The k$_{S}$ indices of a given layer increase as one moves from the periphery to the center of the network [28, 29]. Node size is proportional to the logarithm of the degree of the node. We highlight the 25 inpatients with the largest degree values. Note that inpatients with high k values are not concentrated at the “center” of the network but instead are scattered throughout different k -shells. We highlight the position of the three nodes A, B, and C, of the origins that were used in the example of Fig. 1. c, Scatter plot of the node degree k as a function of k$_{S}$ for all the nodes in the CNI network (black symbols) and the degree-preserving randomized version of the same network (red symbols). Note that there are many inpatients with large k and low k$_{S}$ values in the original network while in the randomized email network all the hubs are located in the inner core of the network. We also show the position of the three origins used in Fig. 1. d, When spreading starts from multiple origins, the set of nodes with highest degree (blue continuous line) can spread significantly more than the set of highest- k$_{S}$ nodes (red continuous line), because in the latter case most of these nodes are connected to each other. If we only consider in this set nodes that are not directly linked, then both the sets of highest k or k$_{S}$ nodes yield a similar result (dashed lines), where spreading is significantly enhanced. Results are shown for β = 3% in the CNI. FIG 4. SIS spreading in the CNI network and β dependence for SIS and SIR. a, b, Virus persistence ρ ( k$_{S}$, k ) as a function of k and k$_{S}$ values of inpatients in the CNI network for, β = 2%, and β = 4%, respectively, where 20% of the individuals are initially infected. The infection survives mainly in nodes with large k$_{S}$ values. c, We form four groups of nodes of the CNI network based on their k -shell values. For all values of β , virus persistence is consistently higher in the inner k -shells. d, Influence of the infection probability β on the spreading efficiency of nodes, grouped according to their k -shell values, for SIR spreading. The solid black line refers to the average infected percentage over all network nodes. Nodes in higher k -shells are consistently the most efficient, independently of the β value.