How community-like is the structure of synthetically generated graphs?

Social-like graph generators have become an indispensable tool when designing proper evaluation methodologies for social graph applications, algorithms and systems. Existing synthetic generators have been designed to produce data with characteristics similar to those found in real graphs, such as power-law degree distributions, a large clustering coefficient or a small diameter. However, real social networks are organized into higher level structures, called communities, that are not explicitly considered by these generators. In this paper, we study the statistical features of the community structure found in real social networks, and compare them to those generated by the LFR and LDBC-DG generators. We found that communities show multimodal features, and thus are hard to generate with simple community models. According to our results LDBC-DG draws realistic community distributions, even reproducing the multimodality observed.