Analysis Problems in the Models on Social Networks in Marketing
Abstract
Analysis Problems in the Models on Social Networks in Marketing
Incoming article date: 18.02.2019A model of impact in a social network is a weighted directed graph. Its vertices correspond to the members of a social group, and its arcs describe their mutual impact. A real value (an opinion of the group's member) as a function of time is ascribed to each vertex, and a real number (weight) is ascribed to each arc (a degree of impact of one member of the group to another or, what is the same, a degree of confidence of one member of the group to another). All strong subgroups (non-degenerated strong components of the digraph) develop their final opinions which depend only to the initial opinions of their members. The final opinions of other members of the group are linear convolutions of the final opininions of all strong subgroups. A number of indices is used for the additional quantitative characteristics of the social group. From the marketing point of view, the solution of the analysis problems provides a segmentation of the target audience for the determination of the most appropriate objects of marketing impact (members of the strong subgroups).
Keywords: directed graphs, differential games, dynamic control models, marketing research, social networks