  The lattice gas model of condensation in a heterogeneous pore system,
represented by a random graph of cells, is studied using an exact analytical
solution. A binary mixture of pore cells with different coordination numbers is
shown to exhibit two phase transitions as a function of chemical potential in a
certain temperature range. Heterogeneity in interaction strengths is
demonstrated to reduce the critical temperature and, for large enough degree of
disorder, divides the cells into ones which are either on average occupied or
unoccupied. Despite treating the pore space loops in a simplified manner, the
random-graph model provides a good description of condensation in porous
structures containing loops. This is illustrated by considering capillary
condensation in a structural model of mesoporous silica SBA-15.
