title: k-core percolation on complex networks: Comparing random, localized, and targeted attacks.
abstract: The type of malicious attack inflicting on networks greatly influences their stability under ordinary percolation in which a node fails when it becomes disconnected from the giant component. Here we study its generalization, k-core percolation, in which a node fails when it loses connection to a threshold k number of neighbors. We study and compare analytically and by numerical simulations of k-core percolation the stability of networks under random attacks (RA), localized attacks (LA) and targeted attacks (TA), respectively. By mapping a network under LA or TA into an equivalent network under RA, we find that in both single and interdependent networks, TA exerts the greatest damage to the core structure of a network. We also find that for Erdős-Rényi (ER) networks, LA and RA exert equal damage to the core structure, whereas for scale-free (SF) networks, LA exerts much more damage than RA does to the core structure.
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Xin
authors.initials: X
authors.lastname: Yuan
authors.affiliation: School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China.
authors.forename: Yang
authors.initials: Y
authors.lastname: Dai
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley
authors.affiliation: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.|Minerva Center and Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
authors.forename: Shlomo
authors.initials: S
authors.lastname: Havlin