References Isaac Chavel, Isoperimetric Inequalities: Differential geometric and analytic persepectives, Cambridge university press, Cambridge, UK (2001), Discusses the topic in the context of manifolds, no mention of graphs. N. Th. Varopoulos, Isoperimetric inequalities and Markov chains, J. Funct. Anal. 63:2 (1985), 215–239. Thierry Coulhon and Laurent Saloff-Coste, Isopérimétrie pour les groupes et les variétés, Rev. Mat. Iberoamericana 9:2 (1993), 293–314. This paper contains the result that on groups of polynomial growth, volume growth and isoperimetric inequalities are equivalent. In French. Fan Chung, Discrete Isoperimetric Inequalities. Surveys in Differential Geometry IX, International Press, (2004), 53–82. http://math.ucsd.edu/~fan/wp/iso.pdf. This paper contains a precise definition of the isoperimetric dimension of a graph, and establishes many of its properties. Mathematical analysis Dimension