  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.
