  The analysis of the results of a depletion code is often considered a tedious
and delicate task for it requires both the processing of large volume of
information (the time dependent composition of up to thousands isomeric states)
and an extensive experience of nuclear reactions and associated nuclear data.
From these observations, dedicated developments have been integrated to the
upcoming version of the Monte Carlo depletion code VESTA 2.2, in order to
implement an innovative representation of depletion problems. The aim is to
provide user with an adapted and efficient framework to ease the analysis of
the results of the code and facilitate their interpretation. This effort
ultimately culminated in the development of the representation of the isotope
evolution of a given system as a directed graph. In this paper, it is shown
that the Bateman equation encoded in the VESTA code indeed possesses a natural
interpretation in terms of directed cyclic graph and it is proposed to explore
some of the insight one can gain from the graph representation of a depletion
problem. Starting from the new capabilities of the code, it is shown how one
can build on the wealth of existing methods of graph theory in order to gain
useful information about the nuclear reactions taking place in a material under
irradiation. The graph representation of a depletion problem being especially
simple in activation problems, for then only a limited number of nuclides and
reactions are involved, the graph representation and its associated tools will
be used to study the evolution of the structure materials of a simplifed model
of the ITER fusion reactor.
