  The Blume-Emery-Griffiths model with a random crystal field is studied in a
random graph architecture, in which the average connectivity is a controllable
parameter. The disordered average over the graph realizations is treated by
replica symmetry formalism of order parameter functions. A self-consistent
equation for the distribution of local fields is derived and numerically solved
by a population dynamics algorithm. The results show that the average
connectivity amounts to changes in the topology of the phase diagrams. Phase
diagrams for representative values of the model parameters are compared with
those obtained for fully connected mean field and renormalization group
approaches.
