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 $e$ 的生成树中心性衡量了 $e$ 对 $\mathcal{G}$ 连通性的重要程度。在实践中，生成树中心性在计算生物学、电气网络和组合优化等领域有着广泛应用。然而，在大型图上计算所有边的生成树中心性极具挑战性。现有技术难以处理此类图，因为它们要么受限于昂贵的矩阵运算，要么需要采样大量长随机游走。为解决这些问题，本文提出了TGT及其增强版本TGT+，这两种算法用于计算所有边的生成树中心性，并提供了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，弥补了先前解决方案的不足。TGT+在TGT的基础上结合随机游走与若干额外启发式优化，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，将TGT+与近期同类算法进行了实验对比。实验结果证明，TGT+在精度不降低的情况下，通常能实现超过一个数量级的加速，显著优于现有技术。