The $\lambda$-entropy of a right-resolving $\lambda$-graph system is introduced as the upper asymptotic growth rate of the number of vertices at level n. It is shown that shift equivalent right-resolving $\lambda$-graph systems have the same $\lambda$-entropy. The $\lambda$-entropies of right-resolving $\lambda$-graph systems that are invariantly associated to subshifts are invariants of topological conjugacy. Finite directed graphs are used in the construction of compact forward separated Shannon graphs that have the structure of a pushdown automaton and that are invariantly associated to the subshift they present. To these compact forward separated Shannon graphs there correspond $\lambda$-graph systems whose $\lambda$-entropy is equal to the topological entropy of the edge shift of the finite directed graph. Examples are given.