Maximizing spreading in complex networks with risk in node activation

It is widely acknowledged that the initial spreaders play an important role in the spread of information in complex networks. Thus, a variety of centrality-based methods have been proposed for identifying the most influential spreaders. However, most existing studies overlook the fact that, in real social networks, it is more costly and difficult to convince influential individuals to act as initial spreaders, resulting in a high risk to maximal spreading. In this paper, we address this problem on the basis of the assumption that the activation of large-degree nodes carries a higher risk than that of small-degree nodes. We aim to identify the initial spreaders that most effectively maximize the spreading when considering both the activation risk and the outbreak size of the initial spreaders. Analysis of random networks reveals that the degree of the optimal initial spreaders does not correspond to the largest node degree in the network, but is instead determined by the infection probability and difference in activation risk among nodes with different degrees. We propose a risk-aware metric to identify the most effective spreaders in real networks. Numerical simulations show that this risk-aware metric outperforms the existing benchmark centralities in terms of maximizing the spreading.