  This thesis presents a local-to-global perspective on graph neural networks
(GNN), the leading architecture to process graph-structured data. After
categorizing GNN into local Message Passing Neural Networks (MPNN) and global
Graph transformers, we present three pieces of work: 1) study the convergence
property of a type of global GNN, Invariant Graph Networks, 2) connect the
local MPNN and global Graph Transformer, and 3) use local MPNN for graph
coarsening, a standard subroutine used in global modeling.
