  Projects are characterised by activity networks with a critical path, a
sequence of activities from start to end, that must be finished on time to
complete the project on time. Watching over the critical path is the project
manager's strategy to ensure timely project completion. This intense focus on a
single path contrasts the broader complex structure of the activity network,
and is due to our poor understanding on how that structure influences this
critical path. Here, we use a generative model and detailed data from 77 real
world projects (plus 10 billion dollars total budget) to demonstrate how this
network structure forces us to look beyond the critical path. We introduce a
duplication-split model of project schedules that yields (i) identical
power-law in- and-out degree distributions and (ii) a vanishing fraction of
critical path activities with schedule size. These predictions are corroborated
in real projects. We demonstrate that the incidence of delayed activities in
real projects is consistent with the expectation from percolation theory in
complex networks. We conclude that delay propagation in project schedules is a
network property and it is not confined to the critical path.
