  We highlight a topological aspect of the graph limit theory. Graphons are
limit objects for convergent sequences of dense graphs. We introduce the
representation of a graphon on a unique metric space and we relate the
dimension of this metric space to the size of regularity partitions. We prove
that if a graphon has an excluded induced sub-bigraph then the underlying
metric space is compact and has finite packing dimension. It implies in
particular that such graphons have regularity partitions of polynomial size.
