  Core-periphery structure is an emerging property of a wide range of complex
systems and indicate the presence of group of actors in the system with an
higher number of connections among them and a lower number of connections with
a sparsely connected periphery. The dynamics of a complex system which is
interacting on a given graph structure is strictly connected with the spectral
properties of the graph itself, nevertheless it is generally extremely hard to
obtain analytic results which will hold for arbitrary large systems. Recently a
statistical ensemble of random graphs with a regular block structure, i.e. the
ensemble of equitable graphs, has been introduced and analytic results have
been derived in the computationally-hard context of graph partitioning and
community detection. In this paper, we present a general analytic result for a
ensemble of equitable core-periphery graphs, yielding a new explicit formula
for the spectral density of networks with core-periphery structure.
