person who is strategically placed in the core of the network will have a significant effect that leads to dissemination through a large fraction of the population. In order to identify the core and the periphery of the network we use the k -shell (also called k -core) decomposition of the network [11–14]. Examining this quantity in a number of real networks allows us to identify the best individual spreaders in the network when the spreading originates in a single node. For the case of a spreading process originating in many nodes simultaneously we show that we can further improve the efficiency by considering spreading origins located at a determined distance from each other. 

We study real-world complex networks that represent archetypical examples of social structures. We investigate (i) the friendship network between 3.4 million members of the LiveJournal.com community [15], (ii) the network of email contacts in the Computer Science Department of the University College London (Zhou, S., private communication), (iii) the contact network of inpatients (CNI) collected from hospitals in Sweden [16], and (iv) the network of actors who have co-starred in movies labeled by imdb.com as adult [17] (see Supplementary Information Section I for details). 

To study the spreading process we apply the Susceptible-Infectious-Recovered (SIR) and Susceptible-Infectious-Susceptible (SIS) models [2, 3, 18] on the above networks (see Methods section). These models have been used to describe disease spreading as well as information and rumor spreading in social processes where an actor constantly needs to be reminded [19]. We denote the probability that an infectious node will infect a susceptible neighbor as β . In our study we use relatively small values for β , so that the infected percentage of the population remains small. In the case of large β values, where spreading can reach a large fraction of the population, the role of individual nodes is no longer important and spreading would cover almost all the network, independently of where it originated from. 

The location of a node in the network is obtained using the k -shell decomposition analysis [11–13]. This process assigns an integer index or coreness, k$_{S}$ , to each node representing its location according to successive layers ( k -shells) in the network. The k$_{S}$ index is a quite robust measure and the nodes ranking is not influenced significantly in the case of incomplete information (for details see SI-Fig. 6 in SI-Section II). Small values of k$_{S}$ define the periphery of the network and the innermost network core corresponds to large k$_{S}$ (see Fig. 1a and SI-Section II). Figures 1b-d illustrate the fact that the size of the population infected in a spreading process (shown in this example in the CNI network) is not necessarily 

