Abstract
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on a social network is a global process, it is commonly believed that measuring the influence of nodes inevitably requires the knowledge of the entire network. Using percolation theory, we show that the spreading process displays a nucleation behavior: Once a piece of information spreads from the seeds to more than a small characteristic number of nodes, it reaches a point of no return and will quickly reach the percolation cluster, regardless of the entire network structure; otherwise the spreading will be contained locally. Thus, we find that, without the knowledge of the entire network, any node's global influence can be accurately measured using this characteristic number, which is independent of the network size. This motivates an efficient algorithm with constant time complexity on the long-standing problem of best seed spreaders selection, with performance remarkably close to the true optimum.