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Statistical ensemble of scale-free random graphs
Open accessAbstract
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is characterized by two global parameters, the fractal and the spectral dimensions, which are explicitly calculated. It is discussed in detail how the geometry of the graphs varies when the weights of the nodes are modified. The stability of the scale-free regime is also considered: when it breaks down, either a scale is spontaneously generated or else, a "singular" node appears and the graphs become crumpled. A new computer algorithm to generate these random graphs is proposed. Possible generalizations are also discussed. In particular, more general ensembles are defined along the same lines and the computer algorithm is extended to arbitrary (degenerate) scale-free random graphs.
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Citations
Cites
Bose-Einstein Condensation in Complex Networks
Bianconi, G., & Barabási, A.-L. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5632 · Cited by 808
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
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-similarity of complex networks
Song, C., Havlin, S., & Makse, H. A. (2005) · Nature · doi:10.1038/nature03248 · Cited by 1,495
Subnets of scale-free networks are not scale-free: Sampling properties of networks
Stumpf, M. P. H., Wiuf, C., & May, R. M. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0501179102 · Cited by 561
Metadata
- Authors
- Burda, Z., Correia, J. D., & Krzywicki, A.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2001-09-24
- Volume
- 64
- Issue
- 4
- Pages
- 046118-046118
- ISSN
- 1063-651X (ISSN-L)
- 1095-3787
- OpenAlex
- W2015652921
- Cited by
- 175
- References
- 1
- FWCI
- 8.59
- Type
- journal article
- Language
- en
- Open access
- green
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- Burda, Z., Correia, J. D., & Krzywicki, A. (2001). Statistical ensemble of scale-free random graphs. Physical Review E. https://doi.org/10.1103/physreve.64.046118
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