  Due to high utility in many applications, from social networks to blockchain
to power grids, deep learning on non-Euclidean objects such as graphs and
manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever
increasing interest. We propose a new L\'evy Flights Graph Convolutional
Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy
Flights into random walks on graphs and, as a result, allows both to accurately
account for the intrinsic graph topology and to substantially improve
classification performance, especially for heterogeneous graphs. Furthermore,
we propose a new preferential P-DropEdge method based on the Girvan-Newman
argument. That is, in contrast to uniform removing of edges as in DropEdge,
following the Girvan-Newman algorithm, we detect network periphery structures
using information on edge betweenness and then remove edges according to their
betweenness centrality. Our experimental results on semi-supervised node
classification tasks demonstrate that the LFGCN coupled with P-DropEdge
accelerates the training task, increases stability and further improves
predictive accuracy of learned graph topology structure. Finally, in our case
studies we bring the machinery of LFGCN and other deep networks tools to
analysis of power grid networks - the area where the utility of GDL remains
untapped.
