  We examine the global organization of heterogeneous equilibrium networks
consisting of a number of well distinguished interconnected
parts--``communities'' or modules. We develop an analytical approach allowing
us to obtain the statistics of connected components and an intervertex distance
distribution in these modular networks, and to describe their global
organization and structure. In particular, we study the evolution of the
intervertex distance distribution with an increasing number of interlinks
connecting two infinitely large uncorrelated networks. We demonstrate that even
a relatively small number of shortcuts unite the networks into one. In more
precise terms, if the number of the interlinks is any finite fraction of the
total number of connections, then the intervertex distance distribution
approaches a delta-function peaked form, and so the network is united.
