In 2005, Haijun Zhou and Reinhard Lipowsky [PNAS 105 (2005) 10052-10057] found through analytical calculations that, scale-free networks with highly heterogeneous vertex-degree profiles will have qualitatively more efficient dynamical properties, if the scale-free exponent of the network is in the tiny range of [2, 2.5). This finding was confirmed by empirical observations: a majority of large social and biological complex networks are scale-free and their scale-free exponents are between 2 and 2.5. However a very important and unsolved question is：How was a highly heterogeneous complex network formed? Are intended optimizations needed? What are the effects of network dynamical processes? In their article “Dynamics-driven evolution to structural heterogeneity in complex networks” [Physica A doi:10.1016/j.physa.2008.10.024 (2008)], Zhen Shao and Haijun Zhou found that, if there is a coupling between the dynamical process on the network and the network evolution, then random and blind local structural mutations, after being cumulated for a long time, may lead to qualitative changes in the global and local structures of the network. Their computer simulation results demonstrated that, the appearance of highly heterogeneous scale-free network structure does not need any special mechanism, but that the weak influence of a dynamical process on network structure can partially determine the direction of network long-term evolution. This article gives people a new angle to understand structural properties of complex networks.

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