  Many complex systems in nature and society can be described in terms of
networks capturing the intricate web of connections among the units they are
made of. A key question is how to interpret the global organization of such
networks as the coexistence of their structural subunits (communities)
associated with more highly interconnected parts. Identifying these a priori
unknown building blocks (such as functionally related proteins, industrial
sectors and groups of people) is crucial to the understanding of the structural
and functional properties of networks. The existing deterministic methods used
for large networks find separated communities, whereas most of the actual
networks are made of highly overlapping cohesive groups of nodes. Here we
introduce an approach to analysing the main statistical features of the
interwoven sets of overlapping communities that makes a step towards uncovering
the modular structure of complex systems. After defining a set of new
characteristic quantities for the statistics of communities, we apply an
efficient technique for exploring overlapping communities on a large scale. We
find that overlaps are significant, and the distributions we introduce reveal
universal features of networks. Our studies of collaboration, word-association
and protein interaction graphs show that the web of communities has non-trivial
correlations and specific scaling properties.
