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The studies based on $A+A \rightarrow \emptyset$ and $A+B\rightarrow\emptyset$ diffusion-annihilation processes have so far been studied onweighted uncorrelated scale-free networks and fractal scale-free networks. Inthe previous reports, it is widely accepted that the segregation of particlesin the processes is introduced by the fractal structure. In this paper, westudy these processes on a family of weighted scale-free networks withidentical degree sequence. We find that the depletion zone and segregation areessentially caused by the disassortative mixing, namely, high-degree nodes tendto connect with low-degree nodes. Their influence on the processes is governedby the correlation between the weight and degree. Our finding suggests both theweight and degree distribution don't suffice to characterize thediffusion-annihilation processes on weighted scale-free networks.

Diffusion-annihilation proecesses in weighted scale-free networks with identical degree sequence