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ELASTICITY: Topological Characterization of Robustness in Complex Networks
Just as a herd of animals relies on its robust social structure to survive in
the wild, similarly robustness is a crucial characteristic for the survival of
a complex network under attack. The capacity to measure robustness in complex
networks defines the resolve of a network to maintain functionality in the
advent of classical component failures and at the onset of cryptic malicious
attacks. To date, robustness metrics are deficient and unfortunately the
following dilemmas exist: accurate models necessitate complex analysis while
conversely, simple models lack applicability to our definition of robustness.
In this paper, we define robustness and present a novel metric, elasticity- a
bridge between accuracy and complexity-a link in the chain of network
robustness. Additionally, we explore the performance of elasticity on Internet
topologies and online social networks, and articulate results
Error and attack tolerance of complex networks
Many complex systems, such as communication networks, display a surprising
degree of robustness: while key components regularly malfunction, local
failures rarely lead to the loss of the global information-carrying ability of
the network. The stability of these complex systems is often attributed to the
redundant wiring of the functional web defined by the systems' components. In
this paper we demonstrate that error tolerance is not shared by all redundant
systems, but it is displayed only by a class of inhomogeneously wired networks,
called scale-free networks. We find that scale-free networks, describing a
number of systems, such as the World Wide Web, Internet, social networks or a
cell, display an unexpected degree of robustness, the ability of their nodes to
communicate being unaffected by even unrealistically high failure rates.
However, error tolerance comes at a high price: these networks are extremely
vulnerable to attacks, i.e. to the selection and removal of a few nodes that
play the most important role in assuring the network's connectivity.Comment: 14 pages, 4 figures, Late
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