  Node classification and graph classification are two graph learning problems
that predict the class label of a node and the class label of a graph
respectively. A node of a graph usually represents a real-world entity, e.g., a
user in a social network, or a document in a document citation network. In this
work, we consider a more challenging but practically useful setting, in which a
node itself is a graph instance. This leads to a hierarchical graph perspective
which arises in many domains such as social network, biological network and
document collection. We study the node classification problem in the
hierarchical graph where a 'node' is a graph instance. As labels are usually
limited, we design a novel semi-supervised solution named SEAL-CI. SEAL-CI
adopts an iterative framework that takes turns to update two modules, one
working at the graph instance level and the other at the hierarchical graph
level. To enforce a consistency among different levels of hierarchical graph,
we propose the Hierarchical Graph Mutual Information (HGMI) and further present
a way to compute HGMI with theoretical guarantee. We demonstrate the
effectiveness of this hierarchical graph modeling and the proposed SEAL-CI
method on text and social network data.
