  We report on phenomena observed in planar integrated networks obtained
connecting superconducting island by Josephson tunnel junctions. These
networks, identifiable as tree-like graphs, have branches consisting of series
arrays of Josephson junctions which can be individually current biased and
characterized. Both Josephson supercurrents and gap parameters of the arrays
embedded in the graph structures display properties significantly different
from those of reference arrays fabricated on the same chips and having
identical geometrical shape. The temperature and magnetic field dependencies of
the Josephson current of the embedded arrays both show a singular behavior when
a critical value is reached by the Josephson characteristic energy. The gap
parameter of the junctions generating the embedded arrays is higher than that
of the junctions forming the reference geometrical arrays.
