  One of the main organizing principles in real-world social, information and
technological networks is that of network communities, where sets of nodes
organize into densely linked clusters. Even though detection of such
communities is of great interest, understanding the structure communities in
large networks remains relatively limited. Due to unavailability of labeled
ground-truth data it is practically impossible to evaluate and compare
different models and notions of communities on a large scale.
  In this paper we identify 6 large social, collaboration, and information
networks where nodes explicitly state their community memberships. We define
ground-truth communities by using these explicit memberships. We then
empirically study how such ground-truth communities emerge in networks and how
they overlap. We observe some surprising phenomena. First, ground-truth
communities contain high-degree hub nodes that reside in community overlaps and
link to most of the members of the community. Second, the overlaps of
communities are more densely connected than the non-overlapping parts of
communities, in contrast to the conventional wisdom that community overlaps are
more sparsely connected than the communities themselves.
  Existing models of network communities do not capture dense community
overlaps. We present the Community-Affiliation Graph Model (AGM), a conceptual
model of network community structure, which reliably captures the overall
structure of networks as well as the overlapping nature of network communities.
