What do real communities in social networks look like? Community detection plays a key role in understanding the structure of real-life 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.