  Existing Graph Neural Networks (GNNs) are limited to process graphs each of
whose vertices is represented by a vector or a single value, limited their
representing capability to describe complex objects. In this paper, we propose
the first GNN (called Graph in Graph Neural (GIG) Network) which can process
graph-style data (called GIG sample) whose vertices are further represented by
graphs. Given a set of graphs or a data sample whose components can be
represented by a set of graphs (called multi-graph data sample), our GIG
network starts with a GIG sample generation (GSG) module which encodes the
input as a \textbf{GIG sample}, where each GIG vertex includes a graph. Then, a
set of GIG hidden layers are stacked, with each consisting of: (1) a GIG
vertex-level updating (GVU) module that individually updates the graph in every
GIG vertex based on its internal information; and (2) a global-level GIG sample
updating (GGU) module that updates graphs in all GIG vertices based on their
relationships, making the updated GIG vertices become global context-aware.
This way, both internal cues within the graph contained in each GIG vertex and
the relationships among GIG vertices could be utilized for down-stream tasks.
Experimental results demonstrate that our GIG network generalizes well for not
only various generic graph analysis tasks but also real-world multi-graph data
analysis (e.g., human skeleton video-based action recognition), which achieved
the new state-of-the-art results on 13 out of 14 evaluated datasets. Our code
is publicly available at
https://github.com/wangjs96/Graph-in-Graph-Neural-Network.
