Network analysis for active and passive propagation models

A large number of studies have been conducted over a long period of time to better understand how people adopt new products and/or ideas. With recent advancement in social network technologies such as Facebook and Twitter, the interest in better understanding the role of social network effect or social influence on the adoption of an idea has again been brought to the forefront. In this study, we examine the propagation of ideas through a social network and we introduce two network propagation rules to explain the idea propagation under social influence. We then apply the rules to different network models, which include a large-world network, a small-world network, a random network, and local neighbor networks such as a path, a star, and their variations. In terms of social network in our study, we say that if a person has adopted an idea, then the person is infected by the idea. So the main interest of our study is to find the minimum number of initially infected individuals (i.e., early adopters of an idea) to effectively infect the rest of the social network. Furthermore, we give examples of real-world situations in management and the spread of violence, where the proposed propagation analysis can be applied. © 2013 Wiley Periodicals, Inc. NETWORKS, Vol. 63(2), 160-169 2014