The paper aims to find equilibrium conditions in connected reaction graphs (reaction networks) consisting of reaction complexes with some special properties. Such graphs often arise when studying complex chemical systems. Connectivity in this case implies the existence of linear stoichiometric relations, including all available complexes, which express material balance restrictions on the graph arcs. The methodology is based on chemical thermodynamics and statistical physics: connected graphs may be considered as an ensemble of chemical states, having their own meta-thermodynamic functions. It is shown that equilibrium composition can be calculated using the analogue of the partition sum. Some numerical examples are presented.