  As Graph Neural Networks (GNNs) are widely adopted in digital pathology,
there is increasing attention to developing explanation models (explainers) of
GNNs for improved transparency in clinical decisions.
  Existing explainers discover an explanatory subgraph relevant to the
prediction.
  However, such a subgraph is insufficient to reveal all the critical
biological substructures for the prediction because the prediction will remain
unchanged after removing that subgraph.
  Hence, an explanatory subgraph should be not only necessary for prediction,
but also sufficient to uncover the most predictive regions for the explanation.
  Such explanation requires a measurement of information transferred from
different input subgraphs to the predictive output, which we define as
information flow.
  In this work, we address these key challenges and propose IFEXPLAINER, which
generates a necessary and sufficient explanation for GNNs.
  To evaluate the information flow within GNN's prediction, we first propose a
novel notion of predictiveness, named $f$-information, which is directional and
incorporates the realistic capacity of the GNN model.
  Based on it, IFEXPLAINER generates the explanatory subgraph with maximal
information flow to the prediction.
  Meanwhile, it minimizes the information flow from the input to the predictive
result after removing the explanation.
  Thus, the produced explanation is necessarily important to the prediction and
sufficient to reveal the most crucial substructures.
  We evaluate IFEXPLAINER to interpret GNN's predictions on breast cancer
subtyping.
  Experimental results on the BRACS dataset show the superior performance of
the proposed method.
