Arbitrary degree distribution networks with perturbations

Complex networks have played an important role in the field of natural science and social science, attracting considerable attention of more and more scholars. Currently, scholars have proposed numbers of complex networks, in which some show a required degree distribution and others follow arbitrary degree distribution. The goal of this paper is to discuss the impact of perturbations on degree distribution. To this end, we first introduce two types of perturbations, i.e., edge perturbations and vertex perturbations, and investigate networks whose structure can be determined by tuning perturbation rules. Next, we calculate the degree distribution using two popularly utilized mathematical methods, namely, rate equation and generating function. Afterward, we analyze several networks with different degree distributions, for example, Poisson distribution, stretched exponential distribution, and power-law distribution; there are, in practice, some pronounced differences among three cases. Therefore, to a certain extent, the above three cases can serve as the measures for degree distribution to help us clearly distinguish among different degree distributions.