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Emergence of tempered preferential attachment from optimization.

ABSTRACT: We show how preferential attachment can emerge in an optimization framework, resolving a long-standing theoretical controversy. We also show that the preferential attachment model so obtained has two novel features, saturation and viability, which have natural interpretations in the underlying network and lead to a power-law degree distribution with exponential cutoff. Moreover, we consider a generalized version of this preferential attachment model with independent saturation and viability, leading to a broader class of power laws again with exponential cutoff. We present a collection of empirical observations from social, biological, physical, and technological networks, for which such degree distributions give excellent fits. We suggest that, in general, optimization models that give rise to preferential attachment with saturation and viability effects form a good starting point for the analysis of many networks.

SUBMITTER: D'Souza RM

PROVIDER: S-EPMC1839059 | biostudies-literature | 2007 Apr

REPOSITORIES: biostudies-literature

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Emergence of tempered preferential attachment from optimization.

D'Souza Raissa M RM Borgs Christian C Chayes Jennifer T JT Berger Noam N Kleinberg Robert D RD

Proceedings of the National Academy of Sciences of the United States of America 20070329 15

We show how preferential attachment can emerge in an optimization framework, resolving a long-standing theoretical controversy. We also show that the preferential attachment model so obtained has two novel features, saturation and viability, which have natural interpretations in the underlying network and lead to a power-law degree distribution with exponential cutoff. Moreover, we consider a generalized version of this preferential attachment model with independent saturation and viability, lea ...[more]

PMID: 17395721

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Project description:BackgroundMany biological networks show some characteristics of scale-free networks. Scale-free networks can evolve through preferential attachment where new nodes are preferentially attached to well connected nodes. In networks which have evolved through preferential attachment older nodes should have a higher average connectivity than younger nodes. Here we have investigated preferential attachment in the context of metabolic networks.ResultsThe connectivities of the enzymes in the metabolic network of Escherichia coli were determined and representatives for these enzymes were located in 11 eukaryotes, 17 archaea and 46 bacteria. E. coli enzymes which have representatives in eukaryotes have a higher average connectivity while enzymes which are represented only in the prokaryotes, and especially the enzymes only present in betagamma-proteobacteria, have lower connectivities than expected by chance. Interestingly, the enzymes which have been proposed as candidates for horizontal gene transfer have a higher average connectivity than the other enzymes. Furthermore, It was found that new edges are added to the highly connected enzymes at a faster rate than to enzymes with low connectivities which is consistent with preferential attachment.ConclusionHere, we have found indications of preferential attachment in the metabolic network of E. coli. A possible biological explanation for preferential attachment growth of metabolic networks is that novel enzymes created through gene duplication maintain some of the compounds involved in the original reaction, throughout its future evolution. In addition, we found that enzymes which are candidates for horizontal gene transfer have a higher average connectivity than other enzymes. This indicates that while new enzymes are attached preferentially to highly connected enzymes, these highly connected enzymes have sometimes been introduced into the E. coli genome by horizontal gene transfer. We speculate that E. coli has adjusted its metabolic network to a changing environment by replacing the relatively central enzymes for better adapted orthologs from other prokaryotic species.

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Emergence of tempered preferential attachment from optimization.

Publications

Emergence of tempered preferential attachment from optimization.

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