A Complexity-Theoretic Analysis of Majority Illusion in Social Networks

Abstract

Majority illusion occurs in a social network when the majority of the network vertices belong to a certain type but the majority of each vertex's neighbours belong to a different type, therefore creating the wrong perception, i.e., the illusion, that the majority type is different from the actual one. From a system engineering point of view, this motivates the search for algorithms to detect and, where possible, correct this often undesirable phenomenon. In this we provide a computational study of majority illusion in social networks, paying particular attention to the problem of its verification, i.e., whether majority illusion can occur on social networks, and elimination, i.e., how can we eliminate majority illusion by social network rewiring. While we show that the problems we consider are generally NP-complete, we also provide a parameterised complexity analysis, showing FPT-algorithms for the detection problem and W[1]-hardness for the elimination problem, using natural graph-theoretic parameters.