Identifying multiple influential spreaders based on generalized closeness centrality

To maximize the spreading influence of multiple spreaders in complex networks, one important fact cannot be ignored: the multiple spreaders should be dispersively distributed in networks, which can effectively reduce the redundance of information spreading. For this purpose, we define a generalized closeness centrality (GCC) index by generalizing the closeness centrality index to a set of nodes. The problem converts to how to identify multiple spreaders such that an objective function has the minimal value. By comparing with the K-means clustering algorithm, we find that the optimization problem is very similar to the problem of minimizing the objective function in the K-means method. Therefore, how to find multiple nodes with the highest GCC value can be approximately solved by the K-means method. Two typical transmission dynamics—epidemic spreading process and rumor spreading process are implemented in real networks to verify the good performance of our proposed method.