5 of M ( k$_{S}$, C$_{B}$ ) in Fig. 2, where C$_{B}$ is the betweenness centrality of a node in the network [9, 10]: the value of C$_{B}$ is not a good predictor for spreading efficiency. To quantify the importance of k$_{S}$ in spreading we calculate the “imprecision functions” ϵ$_{k}$$_{S}$ ( p ), ϵ$_{k}$ ( p ), and ϵ$_{C}$$_{B}$ ( p ). These functions estimate for each of the three indicators k$_{S}$ , k , and C$_{B}$ how close to the optimal spreading is the average spreading of the pN (0 < p < 1) chosen origins in each case, (see Methods and SI-Section IV). The strategy to predict the spreading efficiency of a node based on k$_{S}$ is consistently more accurate than a method based on k in the studied p -range (Fig. 3a). The C$_{B}$ -based strategy gives poor results compared to the other two strategies. Our finding is not specific to the social networks shown in Fig. 2. In SI-Section V we analyze the spreading efficiency in other networks not social in origin, like the Internet at the router level [20], with similar conclusions. The key insight of our finding is that in the studied networks a large number of hubs are located in the peripheral low k$_{S}$ layers (Fig. 3b shows the location of the 25 largest hubs in the CNI, see also SI-Section V) and therefore contribute poorly to spreading. The existence of hubs in the periphery is a consequence of the rich topological structure of real networks. In contrast, in a fully random network obtained by randomly rewiring a real network preserving the degree of each node (such a random network corresponds to the configuration model [21], see SI-Section VI) all the hubs are placed in the core of the network (see the red scatter plot in Fig. 3c) and they contribute equally largely to spreading. In such a randomized structure the same information is contained in the k -shell as in the degree classification since there is a one to one relation between both quantities which is approximately linear, k$_{S}$ ∝ k (Fig. 3c and SI-Fig. 13). Examples of real networks that are similar to a random structure are the network of product space of economic goods [22] and the Internet at the AS level (analyzed in the SI-Section V). Our study highlights the importance of the relative location of a single spreading origin. Next, we address the question of the extent of an epidemic that starts in multiple origins simultaneously. Figure 3d shows the extent of SIR spreading in the CNI network when the outbreak simultaneously starts from the n nodes with the highest degree k or the highest k$_{S}$ index. Even though the high k$_{S}$ nodes are the best single spreaders, in the case of multiple spreading the nodes with highest degree are more efficient than those with highest k$_{S}$ . This result is attributed to the overlap of the infected areas of the different spreaders: large k$_{S}$ nodes tend to be clustered close to each other, while hubs can be more spread in