An Investigation into the Trend Stationarity of Local Characteristics in Media and Social Networks

We studied the evolution of complex social networks over time. The elements of the networks are users, and the connections correspond to the interactions between them. At a particular moment in time, each node of a complex network has such characteristics as its degree, as well as the total degree of its neighbors. Obviously, in the process of network growth, these characteristics are constantly changing due to the fact that new edges are attached to this node or its neighbors. In this paper, we study the dynamics of these characteristics over time for networks generated on the basis of a nonlinear preferential attachment mechanism, and we find both the asymptotics of their expected values and the characteristics of their spread around the mean. In addition, we analyze the behavior of these local characteristics for three real social networks. The applicability of the findings to actual problems in the study of social media in the digital humanities is discussed.