Organization of complex networks without multiple connections
<|reference_start|>Organization of complex networks without multiple connections: We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between $const N^{1/2}$ and $const N^{2/3}$, where $N$ is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cut-off of the distribution of the number of connections and find that its position differs from earlier estimates.<|reference_end|>
@article{dorogovtsev2005organization,
    title={Organization of complex networks without multiple connections},
    author={S.N. Dorogovtsev, J.F.F. Mendes, A.M. Povolotsky, A.N. Samukhin},
    journal={Phys.Rev.Lett. 95 (2005) 195701},
    year={2005},
    doi={10.1103/PhysRevLett.95.195701},
    archivePrefix={arXiv},
    eprint={cond-mat/0505193},
    primaryClass={cond-mat.stat-mech cs.NI hep-lat physics.soc-ph}
}