Topological Robustness

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Definition

Topological robustness is a term used to describe a network that takes a significant amount of damage before it collapses.

"The Internet interprets censorship as damage and routes around it". - John Gilmore

"Intuition tells us that disabling a substantial number of nodes will result in an inevitable functional disintegration of a network. This is certainly true for a random network: if a critical fraction of nodes is removed, a phase transition is observed, breaking the network into tiny, non-communicating islands of nodes. Complex systems, from the cell to the Internet, can be amazingly resilient against component failure, withstanding even the incapacitation of many of their individual components and many changes in external conditions.We have recently learnt that topology has an important role in generating this topological robustness[1].

Scale-free networks do not have a critical threshold for disintegration — they are amazingly robust against accidental failures: even if 80% of randomly selected nodes fail, the remaining 20% still form a compact cluster with a path connecting any two nodes. This is because random failure affects mainly the numerous small degree nodes, the absence of which doesn’t disrupt the network’s integrity[2]. This reliance on hubs, on the other hand, induces a so-called attack vulnerability — the removal of a few key hubs splinters the system into small isolated node clusters.[3]

About the Authors

Albert-László Barabási is the Emil T. Hofman Professor of physics at the University of Notre Dame, USA. His research group introduced the concept of scale-free networks and studied their relevance to biological and communication systems. He obtained his M.Sc. degree in physics in 1991 from Eötvös Loránd University, Budapest, Hungary, and his Ph.D. in 1994 from Boston University, USA. After a year as a postdoctoral fellow at IBM Thomas J. Watson Research Center, USA, he joined the University of Notre Dame in 1995. He is a fellow of the American Physical Society, and the author of the general audience book Linked: The New Science of Networks.

Zoltán Nagy Oltvai is an assistant professor of pathology at Northwestern University’s Feinberg School of Medicine, USA. His clinical interest is molecular pathology and he is the director of diagnostic molecular pathology at the medical school and Northwestern Memorial Hospital. His research group’s interest is the theoretical and experimental study of intracellular molecular interaction networks. He received his M.D. degree from Semmelweiss Medical University, Budapest, Hungary, and did his clinical pathology/molecular biology research residency at Washington University/Barnes Hospital in St. Louis, USA.

References

  1. Source Network Biology - Understanding the Cell's Functional Organization. Albert Laszlo Barabasi, Zoltan Oltvai 2004, 71.
  2. Ibid.
  3. Ibid.