TopoBudget's new graph sparsifier preserves community structure exactly

Researchers constantly re-run community detection on large web and social graphs, but most edges are redundant for this task. Existing sparsification techniques preserve spectral properties, cuts, or a single clustering, yet none maintain the multiscale thresholded connectivity structure—the filtration where groups form at high relevance and merge through weaker bridges. Jianru Shen's TopoBudget tackles exactly this: it selects a budgeted subgraph that preserves the labeled component partition at every threshold, and hence the zero-dimensional persistence diagram, while retaining community evidence for later analyses.

TopoBudget first extracts a tie-aware persistence backbone that enforces this hard constraint, then allocates the remaining edge budget greedily to maximize a backbone-conditioned submodular objective. The paper proves exact partition preservation and monotone submodularity, yielding a (1-1/e) guarantee. On synthetic benchmarks and six real web/social graphs, TopoBudget delivers the strongest community preservation among topology-preserving methods under Louvain, stays competitive under Infomap, incurs zero topology mismatch, and runs substantially faster than an effective-resistance baseline. A no-backbone ablation confirms the mandatory backbone improves average quality while providing exact guarantees.