  Perturbations made to networked systems may result in partial structural
loss, such as a blackout in a power-grid system. Investigating the resultant
disturbance in network properties is quintessential to understand real networks
in action. The removal of nodes is a representative disturbance, but previous
studies are seemingly contrasting about its effect on arguably the most
fundamental network statistic, the degree distribution. The key question is
about the functional form of the degree distributions that can be altered
during node removal or sampling, which is decisive in the remaining
subnetwork's static and dynamical properties. In this work, we clarify the
situation by utilizing the relative entropies with respect to the reference
distributions in the Poisson and power-law form. Introducing general sequential
node removal processes with continuously different levels of hub protection to
encompass a series of scenarios including random removal and preferred or
protective removal of the hub, we classify the altered degree distributions
starting from various power-law forms by comparing two relative entropy values.
From the extensive investigation in various scenarios based on direct
node-removal simulations and by solving the rate equation of degree
distributions, we discover in the parameter space two distinct regimes, one
where the degree distribution is closer to the power-law reference distribution
and the other closer to the Poisson distribution.
