Optimization of robustness of complex networks

Paul, Gerald; Tanizawa, Toshihiro; Havlin, Shlomo; Stanley, H. Eugene

doi:10.1140/epjb/e2004-00112-3

Cited by 177 publications

(104 citation statements)

References 20 publications

(28 reference statements)

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“…Also, the interdependence between the local and global architecture is by no means limited to cellular networks but is expected to apply to all networked systems, from the World Wide Web to transportation and social networks (8)(9)(10)(11)(12)33). Indeed, preliminary results indicate that the analysis described here can be successfully carried out for the Internet topology and other networks (12,34,35) and may have an impact on our understanding of cycles in complex networks as well (36, 37) (A.V., J. G. Oliveira, and A.-L.B., unpublished work).…”

Section: Discussionmentioning

confidence: 99%

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Vázquez

Dobrin

Sergi

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

285

236

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Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the underlying reasons for the variable quantity of different subgraph types, their propensity to form clusters, and their relationship with the networks' global organization remain poorly understood. Here we show that a network's large-scale topological organization and its local subgraph structure mutually define and predict each other, as confirmed by direct measurements in five well studied cellular networks. We also demonstrate the inherent existence of two distinct classes of subgraphs, and show that, in contrast to the low-density type II subgraphs, the highly abundant type I subgraphs cannot exist in isolation but must naturally aggregate into subgraph clusters. The identified topological framework may have important implications for our understanding of the origin and function of subgraphs in all complex networks.aggregation ͉ subgraphs A number of complex biological and nonbiological networks were recently found to contain network motifs, representing elementary interaction patterns between small groups of nodes (subgraphs) that occur substantially more often than would be expected in a random network of similar size and connectivity (1, 2). Theoretical and experimental evidence indicates that at least some of these recurring elementary interaction patterns carry significant information about the given network's function and overall organization (1-4). For example, transcriptional regulatory networks of cells (1, 2, 5, 6), neural networks of C. elegans (2), and some electronic circuits (2) are all information processing networks that contain a significant number of feed-forward loop (FFL) motifs. However, in transcriptional regulatory networks these motifs do not exist in isolation but meld into motif clusters (7), while other networks are devoid of FFLs altogether (2).In general, all subgraphs have two important properties: their topology and the directionality of their links. In cellular networks, these two properties can be clearly separated from each other. In protein-protein interaction (PPI) networks all links are by definition nondirectional. In contrast, in transcriptional regulatory networks information flow between a transcription factor and the operon (gene) regulated by it is almost always unidirectional (1, 2). Metabolic networks occupy an intermediate position between these two extremes, because most, but not all, metabolic reactions are reversible under various growth conditions. Despite the difference in the relative role of link directionality, the large-scale organization of the three different network types is quite similar, most being characterized by a scale-free connectivity distribution and hierarchical modularity (8-12). The only exception is the incoming degree distribution (i.e., the number of transcription factors regulating a target gene) of regulatory...

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Section: Discussionmentioning

confidence: 99%

The topological relationship between the large-scale attributes and local interaction patterns of complex networks

Vázquez

Dobrin

Sergi

et al. 2004

Proc. Natl. Acad. Sci. U.S.A.

285

236

View full text Add to dashboard Cite

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“…Defining the total measure as the sum of the measures against both attacks is also found in earlier literature [24][25][26]. Note that the maximum value of R tot equals to unity for networks with complete robustness in which p c = 0 and S = p for both targeted and random attacks.…”

Section: Robustness Optimizationmentioning

confidence: 71%

Robustness of onionlike correlated networks against targeted attacks

2012

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Recently, it was found by Schneider et al. [Proc. Natl. Acad. Sci. USA, 108, 3838 (2011)], using simulations, that scale-free networks with "onion structure" are very robust against targeted high degree attacks. The onion structure is a network where nodes with almost the same degree are connected. Motivated by this work, we propose and analyze, based on analytical considerations, an onion-like candidate for a nearly optimal structure against simultaneous random and targeted high degree node attacks. The nearly optimal structure can be viewed as a set of hierarchically interconnected random regular graphs, the degrees and populations of whose nodes are specified by the degree distribution. This network structure exhibits an extremely assortative degree-degree correlation and has a close relationship to the "onion structure." After deriving a set of exact expressions that enable us to calculate the critical percolation threshold and the giant component of a correlated network for an arbitrary type of node removal, we apply the theory to the cases of random scale-free networks that are highly vulnerable against targeted high degree node removal. Our results show that this vulnerability can be significantly reduced by implementing this onion-like type of degree-degree correlation without much undermining the almost complete robustness against random node removal. We also investigate in detail the robustness enhancement due to assortative degree-degree correlation by introducing a joint degree-degree probability matrix that interpolates between an uncorrelated network structure and the onion-like structure proposed here by tuning a single control parameter. The optimal values of the control parameter that maximize the robustness against simultaneous random and targeted attacks are also determined. Our analytical calculations are supported by numerical simulations.

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“…This study of large production network robustness contributes to the body of knowledge on robustness of networks that includes related work on the effects of the network structure on system dynamics and robustness [16], and the real-world propagation of economic shocks [17].…”

Section: Discussionmentioning

confidence: 99%