Influence control method on directed weighted signed graphs with deterministic causality

Abstract

Making an incorrect determination or ignoring a factor or interaction in a real-world socioeconomic system can greatly affect the functioning of the entire system, which in turn can lead to misconceptions and incorrect managerial decisions. Considering graph models of socioeconomic systems as the research object, where deterministic causality property is the fundamental characteristic of a graph edge, this study addresses the problem of influence control in models represented by directed weighted signed graphs with deterministic causality on edges. Influence control is considered from the point of view of the choice of influential nodes as points of application of control impacts, providing the possibility of targeted control in real-world socioeconomic systems. The algorithm of influence controls (AIC) is proposed as a tool to identify optimal control impacts. The algorithm maximizes the influence under the control model and uses a system of nonlinear constraints to design conditions for adequate model operation. The contributions made by this study are as follows: (1) the AIC validates the graph representation of the system under study; (2) by using AIC, new knowledge is discovered about important factors (i.e., target, or output) and influencing factors (i.e., impact objects, or input); (3) the appropriate metrics allow for the assessment of the compliance of this result with the degree of codirectionality of the response vector and the basic directionality vector of the system; and (4) the algorithm imposes no restrictions on the direction, sign or range of weights on the edges.