Collective Influence Maximization

The omnipresence of cascading process in complex phenomena makes the identification of a small set of influential units, which is widely believed to trigger the outbreak, always an crucial issue in network science. Formulated as Influence maximization (IM) in 2003, this NP-hard problem has received a multitude of heuristic solutions with diverse angles. However, these methods are often unable to provide reliable solutions, due to the lack of an exact metric for evaluating units' contributions on cascading. In this paper, we address IM from optimal percolation and evaluate units based on the collective influence (CI), a novel metric on structural cohesive power that reflects the contributions of each unit's neighborhood on shaping collective dynamics of units over whole network. We reveal that, under probabilistic diffusion model, the structural influence power (CI value) of each node is a weighted cumulation of the diffusion probabilities from neighbors within certain hop. With the newly formulated metric CI, we propose a novel IM algorithm which chooses seeds with the largest CI values.