Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2010/03/P03003
Keywords
growth processes; network dynamics; random graphs; networks
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Funding
- Junta de Andalucia [FQM-01505]
- Spanish MEC-FEDER [FIS2009-08451]
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It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree-degree correlations and related characteristics, is often not clear, and they may arise from specific functional conditions. We show how it is possible to analyse a very general scenario in which nodes can gain or lose edges according to any (e. g., nonlinear) function of local and/or global degree information. Applying our method to two rather different examples of brain development-synaptic pruning in humans and the neural network of the worm C. Elegans-we find that simple biologically motivated assumptions lead to very good agreement with experimental data. In particular, many nontrivial topological features of the worm's brain arise naturally at a critical point.
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