  The cornerstone of statistical mechanics of complex networks is the idea that
the links, and not the nodes, are the effective particles of the system. Here
we formulate a mapping between weighted networks and lattice gasses, making the
conceptual step forward of interpreting weighted links as particles with a
generalised coordinate. This leads to the definition of the grand canonical
ensemble of weighted complex networks. We derive exact expressions for the
partition function and thermodynamic quantities, both in the cases of global
and local (i.e., node-specific) constraints on density and mean energy of
particles. We further show that, when modelling real cases of networks, the
binary and weighted statistics of the ensemble can be disentangled, leading to
a simplified framework for a range of practical applications.
