Extended SPR for Evolving Networks with Nodes Preferential Deletion

Abstract: 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.