Given a graph $\mathcal{G}$, the spanning centrality (SC) of an edge $e$ measures the importance of $e$ for $\mathcal{G}$ to be connected. In practice, SC has seen extensive applications in computational biology, electrical networks, and combinatorial optimization. However, it is highly challenging to compute the SC of all edges (AESC) on large graphs. Existing techniques fail to deal with such graphs, as they either suffer from expensive matrix operations or require sampling numerous long random walks. To circumvent these issues, this paper proposes TGT and its enhanced version TGT+, two algorithms for AESC computation that offers rigorous theoretical approximation guarantees. In particular, TGT remedies the deficiencies of previous solutions by conducting deterministic graph traversals with carefully-crafted truncated lengths. TGT+ further advances TGT in terms of both empirical efficiency and asymptotic performance while retaining result quality, based on the combination of TGT with random walks and several additional heuristic optimizations. We experimentally evaluate TGT+ against recent competitors for AESC using a variety of real datasets. The experimental outcomes authenticate that TGT+ outperforms the state of the arts often by over one order of magnitude speedup without degrading the accuracy.

翻译：给定图 $\mathcal{G}$，边 $e$ 的生成中心性（SC）衡量 $e$ 对于 $\mathcal{G}$ 保持连通的重要性。在实践中，SC 已在计算生物学、电气网络和组合优化等领域得到广泛应用。然而，在大规模图上计算所有边的 SC（AESC）极具挑战性。现有方法难以处理此类图，因为它们要么需执行昂贵的矩阵运算，要么需采样大量长随机游走。为解决这些问题，本文提出 TGT 及其增强版本 TGT+，两种用于 AESC 计算的算法均提供严格的理论近似保证。具体而言，TGT 通过执行具有精心设计截断长度的确定性图遍历，弥补了先前方法的缺陷。TGT+ 结合 TGT 与随机游走及多项额外启发式优化，在保持结果质量的同时，进一步提升了经验效率与渐近性能。我们使用多种真实数据集对 TGT+ 与近期 AESC 竞争方法进行了实验评估。实验结果表明，TGT+ 在精度不降低的前提下，其加速比常超越现有最优方法一个数量级以上。