Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)

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dc.creatorLi, Lun
dc.creatorAlderson, David
dc.creatorTanaka, Reiko
dc.creatorDoyle, John C.
dc.creatorWillinger, Walter
dc.date2005-01-09
dc.date2005-10-18
dc.date.accessioned2026-07-07T06:37:26Z
dc.date.available2026-07-07T06:37:26Z
dc.descriptionAlthough the ``scale-free'' literature is large and growing, it gives neither a precise definition of scale-free graphs nor rigorous proofs of many of their claimed properties. In fact, it is easily shown that the existing theory has many inherent contradictions and verifiably false claims. In this paper, we propose a new, mathematically precise, and structural definition of the extent to which a graph is scale-free, and prove a series of results that recover many of the claimed properties while suggesting the potential for a rich and interesting theory. With this definition, scale-free (or its opposite, scale-rich) is closely related to other structural graph properties such as various notions of self-similarity (or respectively, self-dissimilarity). Scale-free graphs are also shown to be the likely outcome of random construction processes, consistent with the heuristic definitions implicit in existing random graph approaches. Our approach clarifies much of the confusion surrounding the sensational qualitative claims in the scale-free literature, and offers rigorous and quantitative alternatives.
dc.description44 pages, 16 figures. The primary version is to appear in Internet Mathematics (2005)
dc.identifierhttps://arxiv.org/abs/cond-mat/0501169
dc.identifierhttp://arxiv.org/abs/cond-mat/0501169
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/100393
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subjectNetworking and Internet Architecture
dc.subjectCombinatorics
dc.subjectMolecular Networks
dc.titleTowards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version)
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