  Nested graphs have been used in different applications, for example to
represent knowledge in semantic networks. On the other hand, graphs with cycles
are really important in surface reconstruction, periodic schedule and network
analysis. Also, of particular interest are the cycle basis, which arise in
mathematical and algorithm problems. In this work we develop the concept of
perfectly nested eulerian circuits, exploring some of their properties. The
main result establishes an order isomorphism between some sets of perfectly
nested circuits and equivalence classes over finite binary sequences.
