Correlations between structure and random walk dynamics in directed complex networks

In this letter the authors discuss the relationship between structure and random walk dynamics in directed complex networks, with an emphasis on identifying whether a topological hub is also a dynamical hub. They establish the necessary conditions for networks to be topologically and dynamically fully correlated (e.g., word adjacency and airport networks), and show that in this case Zipf’s law is a consequence of the match between structure and dynamics. They also show that real-world neuronal networks and the world wide web are not fully correlated, implying that their more intensely connected nodes are not necessarily highly active.