Critical effect of dependency groups on the function of networks

Roni Parshani, Sergey V. Buldyrev, Shlomo Havlin

Research output: Contribution to journalArticlepeer-review

246 Scopus citations


Current network models assume one type of links to define the relations between the network entities. However, many real networks can only be correctly described using two different types of relations. Connectivity links that enable the nodes to function cooperatively as a network and dependency links that bind the failure of one network element to the failure of other network elements. Here we present an analytical framework for studying the robustness of networks that include both connectivity and dependency links. We show that a synergy exists between the failure of connectivity and dependency links that leads to an iterative process of cascading failures that has a devastating effect on the network stability. We present exact analytical results for the dramatic change in the network behavior when introducing dependency links. For a high density of dependency links, the network disintegrates in a form of a first-order phase transition, whereas for a low density of dependency links, the network disintegrates in a second-order transition. Moreover, opposed to networks containing only connectivity links where a broader degree distribution results in a more robust network, when both types of links are present a broad degree distribution leads to higher vulnerability.

Original languageEnglish
Pages (from-to)1007-1010
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number3
StatePublished - 18 Jan 2011


  • Complex networks
  • Critical phenomena
  • Erdos-Rényi networks
  • Percolation
  • Scale free networks


Dive into the research topics of 'Critical effect of dependency groups on the function of networks'. Together they form a unique fingerprint.

Cite this