title: Exotic phase transitions of k-cores in clustered networks.
abstract: The giant k-core-maximal connected subgraph of a network where each node has at least k neighbors-is important in the study of phase transitions and in applications of network theory. Unlike Erdős-Rényi graphs and other random networks where k-cores emerge discontinuously for k≥3, we show that transitive linking (or triadic closure) leads to 3-cores emerging through single or double phase transitions of both discontinuous and continuous nature. We also develop a k-core calculation that includes clustering and provides insights into how high-level connectivity emerges.
authors.affiliation: Department of Physics, Boston University, Boston, Massachusetts 02215, USA.|Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors.forename: Uttam
authors.initials: U
authors.lastname: Bhat
authors.affiliation: Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05405, USA.
authors.forename: Munik
authors.initials: M
authors.lastname: Shrestha
authors.affiliation: Santa Fe Institute, Santa Fe, New Mexico 87501, USA.
authors.forename: Laurent
authors.initials: L
authors.lastname: Hébert-Dufresne