  The largest eigenvalue of the adjacency matrix of the networks is a key
quantity determining several important dynamical processes on complex networks.
Based on this fact, we present a quantitative, objective characterization of
the dynamical importance of network nodes and links in terms of their effect on
the largest eigenvalue. We show how our characterization of the dynamical
importance of nodes can be affected by degree-degree correlations and network
community structure. We discuss how our characterization can be used to
optimize techniques for controlling certain network dynamical processes and
apply our results to real networks.
