  The increasing prevalence of large-scale graphs poses a significant challenge
for graph neural network training, attributed to their substantial
computational requirements. In response, graph condensation (GC) emerges as a
promising data-centric solution aiming to substitute the large graph with a
small yet informative condensed graph to facilitate data-efficient GNN
training. However, existing GC methods suffer from intricate optimization
processes, necessitating excessive computing resources. In this paper, we
revisit existing GC optimization strategies and identify two pervasive issues:
1. various GC optimization strategies converge to class-level node feature
matching between the original and condensed graphs, making the optimization
target coarse-grained despite the complex computations; 2. to bridge the
original and condensed graphs, existing GC methods rely on a Siamese graph
network architecture that requires time-consuming bi-level optimization with
iterative gradient computations. To overcome these issues, we propose a
training-free GC framework termed Class-partitioned Graph Condensation (CGC),
which refines the node feature matching from the class-to-class paradigm into a
novel class-to-node paradigm. Remarkably, this refinement also simplifies the
GC optimization as a class partition problem, which can be efficiently solved
by any clustering methods. Moreover, CGC incorporates a pre-defined graph
structure to enable a closed-form solution for condensed node features,
eliminating the back-and-forth gradient descent in existing GC approaches
without sacrificing accuracy. Extensive experiments demonstrate that CGC
achieves state-of-the-art performance with a more efficient condensation
process. For instance, compared with the seminal GC method (i.e., GCond), CGC
condenses the largest Reddit graph within 10 seconds, achieving a 2,680X
speedup and a 1.4% accuracy increase.
