This chapter points out how checking a very simple condition often suffices to show that a dense bipartite graph is a good expander. The check is much easier to apply than the eigenvalue method, though in the cases where both methods are feasible both will give much the same results. The sufficient condition offered in the chapter is derived from a study of pseudo-random graphs. The check involves merely the degrees of vertices and the number of common neighbors of pairs of vertices. In fact it is sufficient to imply the bipartite graph is “pseudo-random.”. © 1989, Elsevier Inc.
Thomason, A. (1989). Dense Expanders and Pseudo-Random Bipartite Graphs. Annals of Discrete Mathematics, 43(C), 381–386. https://doi.org/10.1016/S0167-5060(08)70589-2