%0 Journal Article %1 Dorogovtsev2006KCore %A Dorogovtsev, S. N. %A Goltsev, A. V. %A Mendes, J. F. F. %D 2006 %I American Physical Society %J Physical Review Letters %K phase\_transitions percolation critical-phenomena networks k-core %N 4 %P 040601+ %R 10.1103/physrevlett.96.040601 %T \$k\$-Core Organization of Complex Networks %U http://dx.doi.org/10.1103/physrevlett.96.040601 %V 96 %X 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 z2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z2 diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.

@article{Dorogovtsev2006KCore, abstract = {{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 z2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z2 diverges, the networks contain an infinite sequence of k-cores which are ultrarobust against random damage.}}, added-at = {2019-06-10T14:53:09.000+0200}, author = {Dorogovtsev, S. N. and Goltsev, A. V. and Mendes, J. F. F.}, biburl = {https://www.bibsonomy.org/bibtex/27382589ef011deae3f5e18ec568bf4e0/nonancourt}, citeulike-article-id = {1263642}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=PRLTAO000096000004040601000001\&idtype=cvips\&gifs=yes}, citeulike-linkout-1 = {http://link.aps.org/abstract/PRL/v96/e040601}, citeulike-linkout-2 = {http://dx.doi.org/10.1103/physrevlett.96.040601}, citeulike-linkout-3 = {http://link.aps.org/abstract/PRL/v96/i4/e040601}, citeulike-linkout-4 = {http://link.aps.org/pdf/PRL/v96/i4/e040601}, doi = {10.1103/physrevlett.96.040601}, interhash = {5cfc560065a5d2be9c0dfa194826218f}, intrahash = {7382589ef011deae3f5e18ec568bf4e0}, journal = {Physical Review Letters}, keywords = {phase\_transitions percolation critical-phenomena networks k-core}, month = feb, number = 4, pages = {040601+}, posted-at = {2008-12-01 18:33:51}, priority = {4}, publisher = {American Physical Society}, timestamp = {2019-08-01T16:09:09.000+0200}, title = {{\$k\$-Core Organization of Complex Networks}}, url = {http://dx.doi.org/10.1103/physrevlett.96.040601}, volume = 96, year = 2006 }