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Motivated by the intriguing behavior displayed in a dynamic network thatmodels a population of extreme introverts and extroverts (XIE), we consider thespectral properties of ensembles of random split graph adjacency matrices. Wediscover that, in general, a gap emerges in the bulk spectrum between -1 and 0that contains a single eigenvalue. An analytic expression for the bulkdistribution is derived and verified with numerical analysis. We also examinetheir relation to chiral ensembles, which are associated with bipartite graphs.

Emergence of a spectral gap in a class of random matrices associated with split graphs