منابع مشابه
Scale-free networks are ultrasmall.
We study the diameter, or the mean distance between sites, in a scale-free network, having N sites and degree distribution p(k) proportional, variant k(-lambda), i.e., the probability of having k links outgoing from a site. In contrast to the diameter of regular random networks or small-world networks, which is known to be d approximately ln(N, we show, using analytical arguments, that scale-fr...
متن کاملScale-free networks are rare
A central claim in modern network science is that real-world networks are typically “scale free,” meaning that the fraction of nodes with degree k follows a power law, decaying like k−α, often with 2 < α < 3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. We test the universality of scale-free structure by applying state-of-the-art sta...
متن کاملAll scale-free networks are sparse.
We study the realizability of scale-free networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distributi...
متن کاملHow Scale-Free Are Biological Networks
The concept of scale-free network has emerged as a powerful unifying paradigm in the study of complex systems in biology and in physical and social studies. Metabolic, protein, and gene interaction networks have been reported to exhibit scale-free behavior based on the analysis of the distribution of the number of connections of the network nodes. Here we study 10 published datasets of various ...
متن کاملAre Scale-Free Networks Functionally Robust?
This paper reexamines the claim that biological networks are robust due to their scale-free (SF) architecture, by presenting a basic and simple way to assess the role that this architecture plays in determining network robustness. Studying the error tolerance of the yeast protein-protein interaction network [7] to random node removal using the pertaining knockout data we show that it is only ve...
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ژورنال
عنوان ژورنال: Journal of Mathematical Biology
سال: 2020
ISSN: 0303-6812,1432-1416
DOI: 10.1007/s00285-019-01463-z