  In a recent Letter, Friedman and Landsberg discussed the underlying mechanism
of explosive phase transitions on complex networks [Phys. Rev. Lett. 103,
255701 (2009)]. This Brief Report presents a modest, though more insightful
extension of their arguments. We discuss the implications of their results on
the cluster-size distribution and deduce that, under general conditions, the
percolation transition will be explosive if the mean number of nodes per
cluster diverges in the thermodynamic limit and prior to the transition
threshold. In other words, if, upon increase of the network size n the amount
of clusters in the network does not grow proportionally to n, the percolation
transition is explosive. Simulations and analytical calculations on various
models support our findings.
