Giant components in directed multiplex networks
arXiv:1407.4623 · doi:10.1103/PhysRevE.90.052809
Abstract
We describe the complex global structure of giant components in directed multiplex networks which generalizes the well-known bow-tie structure, generic for ordinary directed networks. By definition, a directed multiplex network contains vertices of one type and directed edges of different types. In directed multiplex networks, we distinguish a set of different giant components based on the existence of directed paths of different types between their vertices, such that for each type of edges, the paths run entirely through only edges of that type. If, in particular, , we define a strongly viable component as a set of vertices, in which for each type of edges, each two vertices are interconnected by at least two directed paths in both directions, running through the edges of only this type. We show that in this case, a directed multiplex network contains, in total, different giant components including the strongly viable component. In general, the total number of giant components is . For uncorrelated directed multiplex networks, we obtain exactly the size and the emergence point of the strongly viable component and estimate the sizes of other giant components.
8 pages, 9 figures
References in corpus (21)
- Catastrophic cascade of failures in interdependent networks
- Random graphs with arbitrary degree distributions and their applications
- Multilayer Networks
- The structure and dynamics of multilayer networks
- Community Structure in Time-Dependent, Multiscale, and Multiplex Networks
- Mathematical Formulation of Multi-Layer Networks
- Interdependent networks: Reducing the coupling strength leads to a change from a first to second order percolation transition
- k-core organization of complex networks
- Avalanche Collapse of Interdependent Network
- Statistical Mechanics of Multiplex Ensembles: Entropy and Overlap
- Giant strongly connected component of directed networks
- Network robustness of multiplex networks with interlayer degree correlations
- Percolation Theory on Interdependent Networks Based on Epidemic Spreading
- Percolation in Multiplex Networks with Overlap
- Percolation in Interdependent and Interconnected Networks: Abrupt Change from Second to First Order Transition
- k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
- Multiple percolation transitions in a configuration model of network of networks
- Generalized percolation in random directed networks
- k-Core percolation on multiplex networks
- Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles
- Weak percolation on multiplex networks