Statistical mechanics of complex networks

Albert, Réka; Barabási, Albert‐László

doi:10.1103/revmodphys.74.47

Cited by 18,116 publications

(15,805 citation statements)

References 165 publications

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“…(See Eq. (36) in Albert and Baraba´si (2002).) The percolation threshold 1 D is very close to the considered connectivity y ¼ 0:005: A comparison with the random data shows that this scale-independent distribution is not due to the dynamics of the system, the only difference being the appearance of larger record clusters in the simulation, as shown in Fig.…”

Section: Clusteringsupporting

confidence: 51%

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Network properties, species abundance and evolution in a model of evolutionary ecology

Anderson

2005

Journal of Theoretical Biology

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We study the evolution of the network properties of a populated network embedded in a genotype space characterized by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution produces two distinct types of network. When a specific genotype is only able to influence a few other genotypes, the ecosystem consists of separate noninteracting clusters (i.e. isolated compartments) in genotype space. When different types may influence a large number of other sites, the network becomes one large interconnected cluster. The distribution of interaction strengths-but not the number of connections-changes significantly with time. We find that the species abundance is only realistic for a high level of species connectivity. This suggests that real ecosystems form one interconnected whole in which selection leads to stronger interactions between the different types. Analogies with niche and neutral theory and assembly models are also considered. r

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Section: Clusteringsupporting

confidence: 51%

“…These correspond to below, near and above the percolation threshold. That is, the point where there is a non-zero probability that all living sites are connected in one dominant cluster (see Albert and Baraba´si (2002) for a review of network models and terminology). A realistic species abundance curve was only obtained above the threshold.…”

Section: Parametersmentioning

confidence: 99%

Network properties, species abundance and evolution in a model of evolutionary ecology

Anderson

2005

Journal of Theoretical Biology

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“…A number of topological features are common to the gene regulatory networks in E. coli and yeast 2,3 . A key common feature is that the number of target genes per transcription factor roughly obeys a power law, which is typical of 'scale-free' networks 19 (Fig. 4a and Supplementary Note online).…”

Section: All Interactions 1409 906mentioning

confidence: 95%

Gene regulatory network growth by duplication

2004

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We are beginning to elucidate transcriptional regulatory networks on a large scale 1 and to understand some of the structural principles of these networks 2,3 , but the evolutionary mechanisms that form these networks are still mostly unknown. Here we investigate the role of gene duplication in network evolution. Gene duplication is the driving force for creating new genes in genomes: at least 50% of prokaryotic genes 4,5 and over 90% of eukaryotic genes 6 are products of gene duplication. The transcriptional interactions in regulatory networks consist of multiple components, and duplication processes that generate new interactions would need to be more complex. We define possible duplication scenarios and show that they formed the regulatory networks of the prokaryote Escherichia coli and the eukaryote Saccharomyces cerevisiae. Gene duplication has had a key role in network evolution: more than one-third of known regulatory interactions were inherited from the ancestral transcription factor or target gene after duplication, and roughly one-half of the interactions were gained during divergence after duplication. In addition, we conclude that evolution has been incremental, rather than making entire regulatory circuits or motifs by duplication with inheritance of interactions.

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“…It is therefore of immediate interest to determine which features are generic properties of large-scale reaction networks and which properties are the consequence of a particular chemistry. For instance, do all large reaction networks exhibit the powerlaw degree distribution that is indicative of small world networks [4,5], as suggested by data reported in [6]? If this hypothesis should prove to be true it immediately raises the question whether there are other significant differences that imply a natural classification of naturally occurring reaction networks.…”

Section: Introductionmentioning

confidence: 99%

A Graph-Based Toy Model of Chemistry

Benkö

Flamm

Stadler

2003

J. Chem. Inf. Comput. Sci.

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Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the "small world" behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the "look-and-feel" of chemistry: Molecules are represented as labeled graphs, i.e., by their structural formulae; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulae; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks: Diels-Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.

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Statistical mechanics of complex networks

Cited by 18,116 publications

References 165 publications

Network properties, species abundance and evolution in a model of evolutionary ecology

Network properties, species abundance and evolution in a model of evolutionary ecology

Gene regulatory network growth by duplication

A Graph-Based Toy Model of Chemistry

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