AI 中文总结
该研究提出生成函数方法推导有向网络巨型强双连通分量（SBC）的大小，分析其渗流行为，发现其与巨型强连通分量（SCC）同阈值出现但增长更慢，并将框架应用于生物网络，揭示连通性等的相互作用。
AI 中文摘要
强连通分量（SCC）表征有向网络的模块化结构，但对单个节点失效脆弱。我们研究强双连通分量（SBC），即移除任意单个节点后每对节点仍相互可达的节点集合，作为更鲁棒的连通性概念。利用生成函数形式，我们推导巨型SBC的大小并分析其在随机节点与连边移除下的渗流行为。结果表明，巨型SBC与巨型SCC在相同阈值处出现，但因连通性要求更严格而增长更缓慢。我们还将该理论框架应用于真实生物网络，包括基因调控网络与神经连接组。该框架为理解复杂有向系统中连通性、冗余性与鲁棒性的相互作用提供了洞见。
英文摘要
Strongly connected components (SCCs) characterize modular structure in directed networks but are fragile to single node failures. We study strongly biconnected components (SBCs), which are the set of nodes in which every node pair remains mutually reachable after the removal of any single node, as a more robust notion of connectivity. Using a generating function formalism, we derive the size of the giant SBC and analyze its percolation behavior under random node and link removal. We show that the giant SBC emerges at the same threshold as the giant SCC but grows more slowly due to stricter connectivity requirements. We also applied our theoretical framework to real-world biological networks including gene regulatory networks and neural connectome. Our framework provides insight into the interplay between connectivity, redundancy, and robustness in complex directed systems.
Comments8 pages, 5 figures
