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认识并进一步探索这类网络至关重要。然而，针对存在节点优先删除特性的网络，因缺乏有效方法，相关研究较为匮乏。本文针对这类优先删除网络，提出了一种扩展的SPR方法（ESPR），用于探讨其关键统计特性，尤其是稳态度分布。与常采用的连续形式方法相比，这种具有理论支撑的方法能够保留网络演化过程中的实际拓扑结构及对应统计特征。通过两个定理，我们证明了ESPR方法在处理节点非均匀删除的演化网络时的有效性；此外，还证明SPR方法是ESPR方法的特例。换言之，ESPR是处理度分布问题的有效框架，甚至具有解决演化网络其他统计特征的潜力。