  Graph neural networks have pushed state-of-the-arts in graph classifications
recently. Typically, these methods are studied within the context of supervised
end-to-end training, which necessities copious task-specific labels. However,
in real-world circumstances, labeled data could be limited, and there could be
a massive corpus of unlabeled data, even from unknown classes as a
complementary. Towards this end, we study the problem of semi-supervised
universal graph classification, which not only identifies graph samples which
do not belong to known classes, but also classifies the remaining samples into
their respective classes. This problem is challenging due to a severe lack of
labels and potential class shifts. In this paper, we propose a novel graph
neural network framework named UGNN, which makes the best of unlabeled data
from the subgraph perspective. To tackle class shifts, we estimate the
certainty of unlabeled graphs using multiple subgraphs, which facilities the
discovery of unlabeled data from unknown categories. Moreover, we construct
semantic prototypes in the embedding space for both known and unknown
categories and utilize posterior prototype assignments inferred from the
Sinkhorn-Knopp algorithm to learn from abundant unlabeled graphs across
different subgraph views. Extensive experiments on six datasets verify the
effectiveness of UGNN in different settings.
