Error and attack tolerance of complex networks

Abstract

Many complex systems display a surprising degree of tolerance against errors. For example, relatively simple organisms grow, persist and reproduce despite drastic pharmaceutical or environmental interventions, an error tolerance attributed to the robustness of the underlying metabolic network. Complex communication networks display a surprising degree of robustness: although key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network. The stability of these and other complex systems is often attributed to the redundant wiring of the functional web defined by the systems' components. Here we demonstrate that error tolerance is not shared by all redundant systems: it is displayed only by a class of inhomogeneously wired networks, called scale-free networks, which include the World-Wide Web, the Internet, social networks and cells. We find that such networks display an unexpected degree of robustness, the ability of their nodes to communicate being unaffected even by unrealistically high failure rates. However, error tolerance comes at a high price in that these networks are extremely vulnerable to attacks (that is, to the selection and removal of a few nodes that play a vital role in maintaining the network's connectivity). Such error tolerance and attack vulnerability are generic properties of communication networks.

Genes regulated by caloric restriction have unique roles within transcriptional networks

“…These implications, however, depend upon the interrelationships between genes, connectivity, network architecture and the phenotype, which are topics of ongoing investigation (Siegal et al, 2007). Given a scale-free topology, network theory suggests that highly connected genes will have an essential role in network operation and organism survival (Albert et al, 2000). This notion predicts that CRdownregulated genes will be involved in fundamental biological processes, which is consistent with the idea that CR influences processes related to growth and energy distribution (Holliday, 1989;Hart and Turturro, 1998;Kirkwood and Shanley, 2005).…”

“…The density of transcriptional networks, therefore, is distributed in non-random fashion, with certain compact regions corresponding to large gene groups with similar expression patterns. This architecture makes networks sensitive to disruption of highly connected hub genes, but has the advantage of imparting resistance to random perturbation (Albert et al, 2000).…”

Bayesian statistical modelling of human protein interaction network incorporating protein disorder information

“…Previously, hubs, as highly interactive nodes occupying central positions in the network, were considered to be essential as they are important for the maintenance of the global network architecture - the scale-free architecture. Removing hubs increases the proportion of unreachable nodes and the shortest path lengthes in the network more than removing non-hubs [58]. The previous definitions of essential nodes in biological networks are based on descriptive measures, in contrast to the generic approach proposed here.…”

Integration of ‘omics’ data in aging research: from biomarkers to systems biology

“…Hence, most nodes have only few connections and few nodes have many connections. These highly connected nodes are called hubs (Albert et al ., 2000; Jeong et al ., 2001). Several other measures exist to describe the topology of networks and topological features of nodes.…”