Integer Optimization Model of Dynamic Interactions in Social Networks

Abstract

A social network represents a social structure containing a set of people or groups of people, with some pattern of interactions or ties between them. In most general representation, a social network can be viewed as a network of nodes (people) related to one another using edges (relationship). People interact with different numbers of individuals and with some individuals more than others and this affects behavior in fundamental ways. In reality the characteristic of the interactions is dynamic. The concept of centrality is used to measure the importance of a node’s position in the network. In order to show the dynamic nature of a node the concepts of reciprocity and transitivity are used. In the optimization formulation, this paper proposes an integer linear programming model to analyze the dynamic interactions in the social networks. A feasible neighborhood search is used to solve the model. The result shows the optimal degree of dynamic interactions of a node.