k-core organization of complex networks
<|reference_start|>k-core organization of complex networks: We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.<|reference_end|>
@article{dorogovtsev2005k-core,
    title={k-core organization of complex networks},
    author={S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes},
    journal={Phys. Rev. Lett. 96, 040601 (2006)},
    year={2005},
    doi={10.1103/PhysRevLett.96.040601},
    archivePrefix={arXiv},
    eprint={cond-mat/0509102},
    primaryClass={cond-mat.stat-mech cs.NI math-ph math.MP physics.soc-ph}
}