  Graph condensation, which reduces the size of a large-scale graph by
synthesizing a small-scale condensed graph as its substitution, has immediate
benefits for various graph learning tasks. However, existing graph condensation
methods rely on the joint optimization of nodes and structures in the condensed
graph, and overlook critical issues in effectiveness and generalization
ability. In this paper, we advocate a new Structure-Free Graph Condensation
paradigm, named SFGC, to distill a large-scale graph into a small-scale graph
node set without explicit graph structures, i.e., graph-free data. Our idea is
to implicitly encode topology structure information into the node attributes in
the synthesized graph-free data, whose topology is reduced to an identity
matrix. Specifically, SFGC contains two collaborative components: (1) a
training trajectory meta-matching scheme for effectively synthesizing
small-scale graph-free data; (2) a graph neural feature score metric for
dynamically evaluating the quality of the condensed data. Through training
trajectory meta-matching, SFGC aligns the long-term GNN learning behaviors
between the large-scale graph and the condensed small-scale graph-free data,
ensuring comprehensive and compact transfer of informative knowledge to the
graph-free data. Afterward, the underlying condensed graph-free data would be
dynamically evaluated with the graph neural feature score, which is a
closed-form metric for ensuring the excellent expressiveness of the condensed
graph-free data. Extensive experiments verify the superiority of SFGC across
different condensation ratios.
