Beyond Blocks: Hyperbolic Community Detection

What do real communities in social networks look like? Community detection plays a key role in understanding the structure of reallife graphs with impact on recommendation systems, load balancing and routing. Previous community detection methods look for uniform blocks in adjacency matrices. However, after studying four real networks with ground-truth communities, we provide empirical evidence that communities are best represented as having an hyperbolic structure. We detail HyCoM the Hyperbolic Community Model as a better representation of communities and the relationships between their members, and show improvements in compression compared to standard methods. We also introduce HyCoM-FIT, a fast, parameter free algorithm to detect communities with hyperbolic structure. We show that our method is effective in finding communities with a similar structure to self-declared ones. We report findings in real social networks, including a community in a blogging platform with over 34 million edges in which more than 1000 users established over 300 000 relations.