This paper describes the classi cation of the n-fold symmetric product of a finite graph by means of its homotopy type.This paper describes the classi cation of the n-fold symmetric product of a finite graph by means of its homotopy type, having as universal models the n-fold symmetric product of the wedge of n-circles; and introduces a CW-complex called binomial torus, which is homeomorphic to a space that is a strong deformation retract of the second symmetric products of the wedge of n-circles. Applying the above we calculate the fundamental group, Euler characteristic, homology and cohomology groups of the second symmetric product of finite graphs
