Complex networks have been used to model almost any
real-world complex systems. An especially important
issue regards how to related their structure and dynamics,
which contributes not only for the better understanding of
such systems, but also to the prediction of important
dynamical properties from specific topological features.
In this talk I revise related research developed recently
in my group. Particularly attention is given to the concept
of accessibility, a new measurement integrating topology
and dynamics, and the relationship between frequency of
visits and node degree in directed modular complex
networks. Analytical results are provided that allow accurate
prediction of correlations between structure and dynamics
in systems underlain by directed diffusion. The methodology
is illustrated with respect to the macaque cortical network.