%0 Journal Article %1 Valdez2013Triple %A Valdez, L. D. %A Macri, P. A. %A Stanley, H. E. %A Braunstein, L. A. %D 2013 %J Physical Review E %K interdependent-networks critical-phenomena correlations %N 5 %P 050803(R)+ %R 10.1103/PhysRevE.88.050803 %T Triple point in correlated interdependent networks %U http://dx.doi.org/10.1103/PhysRevE.88.050803 %V 88 %X Many real-world networks depend on other networks, often in non-trivial ways, to keep their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction \$1-p\$ of nodes in one network randomly fail, the damage propagates to nodes in networks that are interdependent and a dynamic cascade of failure occurs that affects the entire system. We present novel dynamic equations for two interdependent networks that allow us to reproduce the cascades of failure for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction \$\alpha\$ of the higher degree nodes on each network. We find a rich phase diagram in the plane \$p-\alpha\$, with a tricritical point reminiscent of the tricritical point of liquids that separates a non-functional phase from two functional phases.

@article{Valdez2013Triple, abstract = {{Many real-world networks depend on other networks, often in non-trivial ways, to keep their functionality. These interdependent "networks of networks" are often extremely fragile. When a fraction \$1-p\$ of nodes in one network randomly fail, the damage propagates to nodes in networks that are interdependent and a dynamic cascade of failure occurs that affects the entire system. We present novel dynamic equations for two interdependent networks that allow us to reproduce the cascades of failure for an arbitrary pattern of interdependency. We study the "rich club" effect found in many real interdependent network systems in which the high-degree nodes are extremely interdependent, correlating a fraction \$\alpha\$ of the higher degree nodes on each network. We find a rich phase diagram in the plane \$p-\alpha\$, with a tricritical point reminiscent of the tricritical point of liquids that separates a non-functional phase from two functional phases.}}, added-at = {2019-06-10T14:53:09.000+0200}, archiveprefix = {arXiv}, author = {Valdez, L. D. and Macri, P. A. and Stanley, H. E. and Braunstein, L. A.}, biburl = {https://www.bibsonomy.org/bibtex/22e4bdbad4fecad8f172234db8cc366ed/nonancourt}, citeulike-article-id = {12594025}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRevE.88.050803}, citeulike-linkout-1 = {http://arxiv.org/abs/1308.4216}, citeulike-linkout-2 = {http://arxiv.org/pdf/1308.4216}, day = 27, doi = {10.1103/PhysRevE.88.050803}, eprint = {1308.4216}, interhash = {843688e5df7c2781fd0c0c26b28cb0dd}, intrahash = {2e4bdbad4fecad8f172234db8cc366ed}, issn = {1550-2376}, journal = {Physical Review E}, keywords = {interdependent-networks critical-phenomena correlations}, month = nov, number = 5, pages = {050803(R)+}, posted-at = {2013-08-24 15:29:07}, priority = {2}, timestamp = {2019-08-01T16:14:30.000+0200}, title = {{Triple point in correlated interdependent networks}}, url = {http://dx.doi.org/10.1103/PhysRevE.88.050803}, volume = 88, year = 2013 }