  As two main focuses of the study of complex networks, the community structure
and the dynamics on networks have both attracted much attention in various
scientific fields. However, it is still an open question how the community
structure is associated with the dynamics on complex networks. In this paper,
through investigating the diffusion process taking place on networks, we
demonstrate that the intrinsic community structure of networks can be revealed
by the stable local equilibrium states of the diffusion process. Furthermore,
we show that such community structure can be directly identified through the
optimization of the conductance of network, which measures how easily the
diffusion occurs among different communities. Tests on benchmark networks
indicate that the conductance optimization method significantly outperforms the
modularity optimization methods at identifying the community structure of
networks. Applications on real world networks also demonstrate the
effectiveness of the conductance optimization method. This work provides
insights into the multiple topological scales of complex networks, and the
obtained community structure can naturally reflect the diffusion capability of
the underlying network.
