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.
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机译：到目前为止，基于$ A + A \ rightarrow \ emptyset $和$ A + B \ rightarrow \ emptyset $扩散-灭过程的研究已在加权不相关的无标度网络和分形无标度网络上进行了研究。在先前的报道中，过程中的颗粒偏析是通过分形结构引入的，这一点已被广泛接受。在本文中，对具有相同程度序列的加权无标度网络族进行这些过程的研究。我们发现，耗尽区和偏析本质上是由杂化混合引起的，即高度节点倾向于与低度节点相连。它们对过程的影响取决于重量和程度之间的相关性。我们的发现表明，权重和度分布都不足以表征加权无标度网络上的扩散-灭过程。
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