Mapping the Structure of Directed Networks: Beyond the "Bow-tie" Diagram

Abstract

We reveal a hierarchical, multilayer organization of finite components -- i.e., tendrils and tubes -- around the giant connected components in directed networks and propose efficient algorithms allowing one to uncover the entire organization of key real-world directed networks, such as the World Wide Web, the neural network of \emph{Caenorhabditis elegans}, and others. With increasing damage, the giant components decrease in size while the number and size of tendril layers increase, enhancing the susceptibility of the networks to damage.

5 pages, 4 figures

References in corpus (1)

• Percolation on sparse networks

Cited by in corpus (9)

• Network structural origin of instabilities in large complex systems
• Sensitivity of directed networks to the addition and pruning of edges and vertices
• Dynamical Mean-Field Theory of Complex Systems on Sparse Directed Networks
• Extended-range percolation in complex networks
• Large order fluctuations, switching, and control in complex networks
• On the accuracy of message-passing approaches to percolation in complex networks
• Connected components in networks with higher-order interactions
• Simple estimation of hierarchical positions and uncertainty in networks of asymmetric interactions
• Topological Components in a Community Currency Network