  Consensus about the universality of the power law feature in complex networks
is experiencing profound challenges. To shine fresh light on this controversy,
we propose a generic theoretical framework in order to examine the power law
property. First, we study a class of birth-and-death networks that is
ubiquitous in the real world, and calculate its degree distributions. Our
results show that the tails of its degree distributions exhibits a distinct
power law feature, providing robust theoretical support for the ubiquity of the
power law feature. Second, we suggest that in the real world two important
factors, network size and node disappearance probability, point to the
existence of the power law feature in the observed networks. As network size
reduces, or as the probability of node disappearance increases, then the power
law feature becomes increasingly difficult to observe. Finally, we suggest that
an effective way of detecting the power law property is to observe the
asymptotic (limiting) behaviour of the degree distribution within its effective
intervals.
