  The analysis of data such as graphs has been gaining increasing attention in
the past years. This is justified by the numerous applications in which they
appear. Several methods are present to predict graphs, but much fewer to
quantify the uncertainty of the prediction. The present work proposes an
uncertainty quantification methodology for graphs, based on conformal
prediction. The method works both for graphs with the same set of nodes
(labelled graphs) and graphs with no clear correspondence between the set of
nodes across the observed graphs (unlabelled graphs). The unlabelled case is
dealt with the creation of prediction sets embedded in a quotient space. The
proposed method does not rely on distributional assumptions, it achieves
finite-sample validity, and it identifies interpretable prediction sets. To
explore the features of this novel forecasting technique, we perform two
simulation studies to show the methodology in both the labelled and the
unlabelled case. We showcase the applicability of the method in analysing the
performance of different teams during the FIFA 2018 football world championship
via their player passing networks.
