AI 中文总结
TopoBudget是一种保持持久连通性的Web图稀疏化方法，通过提取感知边的持久主干并分配预算，实现多尺度连通性与可复用社区分析，在社区保持和运行效率上优于现有方法。
AI 中文摘要
针对Web图和社交图的社区结构会被反复分析的需求，其大量边对该分析而言是冗余的，因此需要进行稀疏化。现有稀疏化方法会保持谱量、割集、局部相似度或单一聚类，但均未保持边相关过滤的阈值连通性结构，该结构是高相关度下群组形成并通过较弱桥接合并的多尺度模式。我们研究保持持久连通性的稀疏化：给定图、边相关过滤及预处理时计算的代理划分，选择预算内子图，该子图在每个阈值下保持标记组件划分，因此保持零维持久图，同时为后续分析保留社区证据。我们的方法TopoBudget首先提取感知边的持久主干以强制执行该约束，然后通过贪婪最大化受主干约束的子模目标来分配剩余边预算，该目标奖励代理内部度的均衡恢复。我们证明其在每个阈值下精确保持组件划分，且受约束的目标是单调且子模的，因此贪婪算法对固定主干的剩余问题可达到(1-1/e)的保证。在保留的合成基准及六个真实Web和社交图上，相同预算下TopoBudget在Louvain算法下的拓扑保持方法中实现最强社区保持，在Infomap算法下仍具竞争力，零拓扑不匹配，且运行速度远快于有效电阻基线。无主干 ablation实验显示，在真实图上，强制主干提升了平均质量并提供精确保证。因此TopoBudget将精确的多尺度连通性与预算内可复用的社区分析相结合。
英文摘要
Web and social graphs are analyzed repeatedly for community structure, yet many of their edges are redundant for this purpose, which motivates sparsification. Existing sparsifiers preserve spectral quantities, cuts, local similarity, or a single clustering, but none preserves the thresholded connectivity structure of an edge-relevance filtration, the multiscale pattern by which groups form at high relevance and merge through weaker bridges. We study persistent-connectivity-preserving sparsification: given a graph, an edge-relevance filtration, and a proxy partition computed once during preprocessing, select 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. Our method, TopoBudget, first extracts a tie-aware persistence backbone that enforces this constraint, then allocates the residual edge budget by greedily maximizing a backbone-conditioned submodular objective that rewards balanced recovery of proxy-internal degree. We prove exact preservation of the component partition at every threshold, and that the conditioned objective is monotone and submodular, so greedy attains a (1-1/e) guarantee for the fixed-backbone residual problem. On held-out synthetic benchmarks and six real Web and social graphs at equal budget, TopoBudget gives the strongest community preservation among topology-preserving methods under Louvain, remains competitive under Infomap, incurs zero topology mismatch, and runs substantially faster than an effective-resistance baseline. A no-backbone ablation shows that, on the real graphs, the mandatory backbone improves average quality while providing the exact guarantee. TopoBudget thus couples exact multiscale connectivity with budgeted, reusable community preservation.
CommentsAccepted at the main research track of WISE 2026 (26th International Conference on Web Information Systems Engineering)
