  A quantitative evaluation of the contribution of individual units in
producing the collective behavior of a complex network can allow us to
understand the potential damage to the structure integrity due to the failure
of local nodes. Given time series for the units, a natural way to do this is to
find the information flowing from the unit of concern to the rest of the
network. In this study, we show that this flow can be rigorously derived in the
setting of a continuous-time dynamical system. With a linear assumption, a
maximum likelihood estimator can be obtained, allowing us to estimate it in an
easy way. As expected, this "cumulative information flow" does not equal to the
sum of the information flows to other individual units, reflecting the
collective phenomenon that a group is not the addition of the individual
members. For the purpose of demonstration and validation, we have examined a
network made of Stuart-Landau oscillators. Depending on the topology, the
computed information flow may differ. In some situations, the most crucial
nodes for the network are not the hubs; they may have low degrees, and, if
depressed or attacked, will cause the failure of the entire network.
