Time-dependent influence metric for cascade dynamics on networks

An algorithm for efficiently calculating the expected size of single-seed cascade dynamics on networks is proposed and tested. The expected size is a time-dependent quantity and so enables the identification of nodes who are the most influential early or late in the spreading process. The measure is accurate for both critical and subcritical dynamic regimes and so generalises the nonbacktracking centrality that was previously shown to successfully identify the most influential single spreaders in a model of critical epidemics on networks.