K-core Organization of Complex Networks

@article{Dorogovtsev2006KcoreOO,
  title={K-core Organization of Complex Networks},
  author={Sergey N. Dorogovtsev and Alexander V. Goltsev and Jos{\'e} F. F. Mendes},
  journal={Physical review letters},
  year={2006},
  volume={96 4},
  pages={
          040601
        }
}
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 birthpoints--the bootstrap percolation thresholds. We show that in networks with a finite mean number zeta2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if… 

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