  We prove that if two nonnegative matrices are strong shift equivalent, the
associated stable Cuntz-Krieger algebras with generalized gauge actions are
conjugate. The proof is done by a purely functional analytic method and based
on constructing imprimitivity bimodule from bipartite directed graphs through
strong shift equivalent matrices, so that we may clarify K-theoretic behavior
of the stable conjugacy between the associated stable Cuntz-Krieger algebras.
We also examine our machinery for the matrices obtained by state splitting
graphs, so that topological conjugacy of the topological Markov shifts is
described in terms of some equivalence relation of the Cuntz-Krieger algebras
with canonical masas and the gauge actions without stabilization.
