  We introduce an intuitive model that describes both the emergence of
community structure and the evolution of the internal structure of communities
in growing social networks. The model comprises two complementary mechanisms:
One mechanism accounts for the evolution of the internal link structure of a
single community, and the second mechanism coordinates the growth of multiple
overlapping communities. The first mechanism is based on the assumption that
each node establishes links with its neighbors and introduces new nodes to the
community at different rates. We demonstrate that this simple mechanism gives
rise to an effective maximal degree within communities. This observation is
related to the anthropological theory known as Dunbar's number, i.e., the
empirical observation of a maximal number of ties which an average individual
can sustain within its social groups. The second mechanism is based on a
recently proposed generalization of preferential attachment to community
structure, appropriately called structural preferential attachment (SPA). The
combination of these two mechanisms into a single model (SPA+) allows us to
reproduce a number of the global statistics of real networks: The distribution
of community sizes, of node memberships and of degrees. The SPA+ model also
predicts (a) three qualitative regimes for the degree distribution within
overlapping communities and (b) strong correlations between the number of
communities to which a node belongs and its number of connections within each
community. We present empirical evidence that support our findings in real
complex networks.
