Speaker
Description
Strongly connected components (SCCs) are essential for identifying modular structures in directed networks. However, they are inherently fragile, as the removal of even a single node can fragment the component and compromise its functionality. To address this limitation and better capture structural stability, we study strongly bi-connected components (SBCs), subgraphs where every pair of nodes is linked by at least two vertex-independent directed paths in both directions. Using a generating function formalism, we develop an analytical framework to estimate the size of the largest SBC in directed random graphs. Our analysis reveals that while the largest SBC emerges at the same threshold as SCC, they grow more gradually due to stricter connectivity requirements. These findings suggest that SBCs offer a more robust framework for modularity, with implications for failure-tolerant design and biological network dynamics.
