  The richness in the content of various information networks such as social
networks and communication networks provides the unprecedented potential for
learning high-quality expressive representations without external supervision.
This paper investigates how to preserve and extract the abundant information
from graph-structured data into embedding space in an unsupervised manner. To
this end, we propose a novel concept, Graphical Mutual Information (GMI), to
measure the correlation between input graphs and high-level hidden
representations. GMI generalizes the idea of conventional mutual information
computations from vector space to the graph domain where measuring mutual
information from two aspects of node features and topological structure is
indispensable. GMI exhibits several benefits: First, it is invariant to the
isomorphic transformation of input graphs---an inevitable constraint in many
existing graph representation learning algorithms; Besides, it can be
efficiently estimated and maximized by current mutual information estimation
methods such as MINE; Finally, our theoretical analysis confirms its
correctness and rationality. With the aid of GMI, we develop an unsupervised
learning model trained by maximizing GMI between the input and output of a
graph neural encoder. Considerable experiments on transductive as well as
inductive node classification and link prediction demonstrate that our method
outperforms state-of-the-art unsupervised counterparts, and even sometimes
exceeds the performance of supervised ones.
