Percolation of a general network of networks

Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene; Xu, Xiaoming; Havlin, Shlomo
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that the damage in the network due to a failure is a continuous function of the fraction of failed nodes. In sharp contrast, in NetONet, due to the cascading failures, the percolation transition may be discontinuous and even a single node failure may lead to abrupt collapse of the system. We demonstrate our general framework for a NetONet composed of \$n\$ classic Erd$\backslash$H\{o\}s-R$\backslash$'\{e\}nyi (ER) networks, where each network depends on the same number \$m\$ of other networks, i.e., a random regular network of interdependent ER networks. In contrast to a $\backslash$emph\{treelike\} NetONet in which the size of the largest connected cluster (mutual component) depends on \$n\$, the loops in the RR NetONet cause the largest connected cluster to depend only on \$m\$. We also analyzed the extremely vulnerable feedback condition of coupling. In the case of ER networks, the NetONet only exhibits two phases, a second order phase transition and collapse, and there is no first phase transition regime unlike the no feedback condition. In the case of NetONet composed of RR networks, there exists a first order phase transition when \$q\$ is large and second order phase transition when \$q\$ is small. Our results can help in designing robust interdependent systems.
Research areas:
Year:
2013
Type of Publication:
Article
Journal:
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume:
88
Number:
6
Pages:
1-13
ISSN:
1539-3755
DOI:
10.1103/PhysRevE.88.062816
Hits: 3837

We use cookies to improve our website and your experience when using it. Cookies used for the essential operation of this site have already been set. To find out more about the cookies we use and how to delete them, see our privacy policy.

  I accept cookies from this site.
EU Cookie Directive Module Information