Evolving networks are more widely existed in real world than static networks, and studying their statistical characteristics is vital to recognize and explore them further. But for the networks with nodes preferential deletion, there are few researches due to the lack of effective methods. In this article, we propose an extended SPR (ESPR) for these preferential removal networks when discuss the essential statistics, especially the steady-state degree distribution. Comparing with continuum formalism that is often employed, this theory-supported method retains the actual topological structure and corresponding statistics of networks during evolving process. With two theorems, we demonstrate the effectiveness of ESPR in handling evolving networks with nodes non-uniform removal; moreover, it also be proved that the SPR is special case of ESPR. In other words, ESPR is an operative framework when deal with the degree distibution, and it even have potential to solve other statistics of evolving networks.
翻译：演化网络在现实世界中比静态网络更为普遍，研究其统计特性对于了解和深入探究其非常重要。但对于存在节点优先删除的网络，由于缺乏有效的方法，因此研究较少。在本文中，我们针对这种节点优先删除的网络提出了扩展SPR（ESPR）方法，在讨论网络的基本统计特性，特别是稳定状态的度分布时使用。与通常采用的连续体形式不同，这个基于理论支持的方法在演化过程中保留了实际的拓扑结构及其相应的统计特性。通过两个定理，我们证明了ESPR在处理演化网络中节点非均匀删除方面的效果，此外，还证明了SPR是ESPR的特殊情况。换句话说，ESPR是一个有效的框架，用于处理度分布，它甚至有潜力解决演化网络的其他统计特性。
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