# Interfaces and the edge percolation map of random directed networks.

@article{Serrano2007InterfacesAT, title={Interfaces and the edge percolation map of random directed networks.}, author={M. {\'A}ngeles Serrano and Paolo De Los Rios}, journal={Physical Review E}, year={2007}, volume={76}, pages={056121} }

The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in the strongly connected component and those in the in and out components. Formal equations for the relative sizes in the number of edges of these giant structures are derived for arbitrary joint degree distributions in the presence of local and two-point… Expand

#### 9 Citations

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#### References

SHOWING 1-10 OF 51 REFERENCES

Percolation in directed scale-free networks.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The percolation properties of directed scale-free networks with correlated in and out degree distributions are studied, derived from a phase diagram that indicates the existence of three regimes, determined by the values of the degree exponents. Expand

Generalized percolation in random directed networks.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2005

We develop a general theory for percolation in directed random networks with arbitrary two-point correlations and bidirectional edges--that is, edges pointing in both directions simultaneously. These… Expand

Giant strongly connected component of directed networks.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is explained that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one and that the World Wide Web is a directed network. Expand

Anomalous percolation properties of growing networks.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The anomalous phase transition of the emergence of the giant connected component in scale-free networks growing under mechanism of preferential linking is described and exact results for the size and the distribution of vertices among connected components are obtained. Expand

Network robustness and fragility: percolation on random graphs.

- Computer Science, Physics
- Physical review letters
- 2000

This paper studies percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolators, bond percolations, and models in which occupation probabilities depend on vertex degree. Expand

Percolation and epidemic thresholds in clustered networks.

- Mathematics, Physics
- Physical review letters
- 2006

It is found that, although clustering in scale-free networks can strongly affect some percolating properties, such as the size and the resilience of the giant connected component, it cannot restore a finite percolation threshold. Expand

Statistical mechanics of complex networks

- Computer Science, Physics
- ArXiv
- 2001

A simple model based on these two principles was able to reproduce the power-law degree distribution of real networks, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. Expand

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

- Computer Science, Physics
- Proceedings of the National Academy of Sciences of the United States of America
- 2004

It is shown that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. Expand

Random graphs with arbitrary degree distributions and their applications.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is demonstrated that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world, while in others there is a measurable discrepancy between theory and reality, perhaps indicating the presence of additional social structure in the network that is not captured by the random graph. Expand

Epidemic spreading in correlated complex networks.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

A dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node's connectivities finds an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links. Expand