Positive Communities on Signed Graphs That Are Not Echo Chambers: A Clique-Based Approach

An area of research on communities in signed networks aims to find structures in which each user in the graph is connected to other members in their community by more positive edges than negative edges, indicating a positive experience for the user. However, some of these communities are ‘echo chambers', a rising area of concern in modern discourse regarding social media, which contain almost exclusively positive edges indicating all users trust each other with little or no push-back. Here exists an interesting contradiction, when finding a ‘positive’ community often times the resulting structure may be the negative ‘echo chamber’. In this work we propose a signed graph community substructure named the$(\epsilon,\ \phi)$-Clique which is the best of both worlds, where each user is happy to be in their community (indicated by have a proportion of positive edges$\geq\epsilon$for each node) as well as there existing a level of disagreement in the system (indicated by the community having a proportion of negative edges$\geq \phi$). From this definition, we design algorithms to exactly find the Maximum$(\epsilon,\ \phi)$-Clique containing a query user, utilising heuristics to combat the NP-Hard and NP-Hard to approximate nature of the problem. We perform experiments to examine the improvements in efficiency of our algorithms to the proposed baseline as well as examine example community outputs to show the effectiveness of our structure.