  We present and discuss isospectral quantum graphs which are not isometric.
These graphs are the analogues of the isospectral domains in R2 which were
introduced recently and are all based on Sunada's construction of isospectral
domains. After presenting some of the properties of these graphs, we discuss a
few examples which support the conjecture that by counting the nodal domains of
the corresponding eigenfunctions one can resolve the isospectral ambiguity.
