Collective phenomena emerge from the interaction of natural or artificial
units with a complex organization. The interplay between structural patterns
and dynamics might induce functional clusters that, in general, are different
from topological ones. In biological systems, like the human brain, the overall
functionality is often favored by the interplay between connectivity and
synchronization dynamics, with functional clusters that do not coincide with
anatomical modules in most cases. In social, socio-technical and engineering
systems, the quest for consensus favors the emergence of clusters.
Despite the unquestionable evidence for mesoscale organization of many
complex systems and the heterogeneity of their inter-connectivity, a way to
predict and identify the emergence of functional modules in collective
phenomena continues to elude us. Here, we propose an approach based on random
walk dynamics to define the diffusion distance between any pair of units in a
networked system. Such a metric allows to exploit the underlying diffusion
geometry to provide a unifying framework for the intimate relationship between
metastable synchronization, consensus and random search dynamics in complex
networks, pinpointing the functional mesoscale organization of synthetic and
biological systems.Comment: 9 pages, 7 figure