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Giant strongly connected component of directed networks
Open accessAbstract
We describe how to calculate the sizes of all giant connected components of a directed graph, including the strongly connected one. In particular, the World Wide Web is a directed network. The results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out-degree distribution P(k(i),k(o)). We show that if P(k(i),k(o)) does not factorize, the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in- and out-components. The calculations of the relative sizes of all the giant components are demonstrated using the simplest examples. We explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one.
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Citations
Cites
Emergence of Scaling in Random Networks
Barabási, A.-L., & Albert, R. (1999) · Science · doi:10.1126/science.286.5439.509 · Cited by 36,135
Error and attack tolerance of complex networks
Albert, R., Jeong, H., & Barabási, A.-L. (2000) · Nature · doi:10.1038/35019019 · Cited by 7,534
Cited by
Statistical mechanics of complex networks
Albert, R., & Barabási, A.-L. (2002) · Reviews of Modern Physics · doi:10.1103/revmodphys.74.47 · Cited by 20,471
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Epidemic processes in complex networks
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.925 · Cited by 3,697
Critical phenomena in complex networks
Dorogovtsev, S. N., Goltsev, A. V., & Mendes, J. F. F. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1275 · Cited by 2,220
Self-citationThe Network of Global Corporate Control
Vitali, S., Glattfelder, J. B., & Battiston, S. (2011) · PLoS ONE · doi:10.1371/journal.pone.0025995 · Cited by 827
Metadata
- Authors
- Dorogovtsev, S. N., Mendes, J. F. F., & Samukhin, A. N.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2001-07-19
- Volume
- 64
- Issue
- 2
- Pages
- 025101-025101
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2069576934
- Cited by
- 303
- References
- 2
- FWCI
- 3.71
- Type
- journal article
- Language
- en
- Open access
- green
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- Dorogovtsev, S. N., Mendes, J. F. F., & Samukhin, A. N. (2001). Giant strongly connected component of directed networks. Physical Review E. https://doi.org/10.1103/physreve.64.025101
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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