A sequence of graphs with diverging number of nodes is a dense graph sequence
if the number of edges grows approximately as for complete graphs. To each such
sequence a function, called graphon, can be associated, which contains
information about the asymptotic behavior of the sequence. Here we show that
the problem of subdividing a large graph in communities with a minimal amount
of cuts can be approached in terms of graphons and the Γ-limit of the
cut functional, and discuss the resulting variational principles on some
examples. Since the limit cut functional is naturally defined on Young
measures, in many instances the partition problem can be expressed in terms of
the probability that a node belongs to one of the communities. Our approach can
be used to obtain insights into the bisection problem for large graphs, which
is known to be NP-complete.Comment: 25 pages, 5 figure