  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.
