Power-law Strength-Degree Correlation From a Resource-Allocation   Dynamics on Weighted Networks
  Many weighted scale-free networks are known to have a power-law correlation between strength and degree of nodes, which, however, has not been well explicated. We investigate the dynamic behaviors of resource/traffic flow on scale-free networks. The dynamical system will evolve to a kinetic equilibrium state, where the strength, defined by the amount of resource or traffic load, is correlated with the degree in a power-law form with tunable exponent. The analytical results agree with simulations well. 
Qing Ou, Ying-Di Jin, Tao Zhou, Bing-Hong Wang, and Bao-Qun Yin