Influence in social networks: formalization variants

This paper suggests a generalization of previously proposed cases of formalizing the influence of users in online social networks based on the actional model of influence. We consider a number of questions, depending on the answer to each of which the notion of agent's influence should be formalized in slightly different ways: whether all the agent's actions have an impact or only the initial ones; whether the Principal (a control subject) is interested in the impact on the agent’s actions or the impact on the consequences of the agent’s actions; whether the Principal believes that the maximum possible influence on any agent takes the same value or not. We consider various combinations of answers to these questions and provide appropriate variants to formalize the notion of influence. We study the properties of the proposed variants of influence formalization (in particular, monotonicity and additivity of the influence function). Then we give examples of calculating the influence of users of the online social network Reddit and compare different variants of influence formalization.