Abstract
As complex environments, networks may affect dynamic processes on them in various ways. Recent study of transport (diffusive) processes on different networks suggests that larger network complexity leaves more room for the process improvement and optimization. On the other hand, the structure--dynamics interdependence reveals that the
emergent dynamic phenomena on networks can be effectively used for
network diagnostics or as a guide for network re-construction from the empirical data. Here we review certain universal dynamic features (scaling, noise and flow correlations, return-time statistics etc.),
which are characteristic for the diffusive processes on scale-free trees and cyclic correlated scale-free graphs. Results of numerical simulations on large networks will be presented. We also discuss robustness/limits of these findings and point out some open theoretical problems in the field.
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