  Graph Neural Networks (GNNs) are de facto solutions to structural data
learning. However, it is susceptible to low-quality and unreliable structure,
which has been a norm rather than an exception in real-world graphs. Existing
graph structure learning (GSL) frameworks still lack robustness and
interpretability. This paper proposes a general GSL framework, SE-GSL, through
structural entropy and the graph hierarchy abstracted in the encoding tree.
Particularly, we exploit the one-dimensional structural entropy to maximize
embedded information content when auxiliary neighbourhood attributes are fused
to enhance the original graph. A new scheme of constructing optimal encoding
trees is proposed to minimize the uncertainty and noises in the graph whilst
assuring proper community partition in hierarchical abstraction. We present a
novel sample-based mechanism for restoring the graph structure via node
structural entropy distribution. It increases the connectivity among nodes with
larger uncertainty in lower-level communities. SE-GSL is compatible with
various GNN models and enhances the robustness towards noisy and heterophily
structures. Extensive experiments show significant improvements in the
effectiveness and robustness of structure learning and node representation
learning.
