Enumerating the Nash equilibria of a game is a known problem of game theory. We take into account twoplayer extensive-form games with perfect information and perfect recall. Based on the notion of compatibility of strategies, a new graph representation permits to devise a new lightweight algorithm to enumerate all of its Nash equilibria. It is the first of its kind not to use brute force. The method provides also intermediate results, like upper (lower) bounds to the value of the utility of Nash equilibria or the enumeration of Nash equilibria that fulfill any given constraints (possibly, unconstrained) on their values. We compare our method to the only existing formulation providing an upper bound to the value of the utility of any Nash equilibrium. The experiments show that our method is faster by some orders of magnitude. We also test the method to enumerate the Nash equilibria on a new library, that we introduce as benchmark for representing all structures and properties of extensive-form games.