Fluctuations of motifs and non-self-averaging in complex networks: A self- vs. non-self-averaging phase transition scenario

Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been observed when the exponent γ of the associated power-law degree...

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Bibliographic Details
Published in:Europhysics letters 2014-01, Vol.105 (2), p.28005-p1-28005-p6
Main Author: Ostilli, M.
Format: Article
Language:English
Subjects:
05.40.-a
89.75.Fb
89.75.Hc
Density
Fluctuation
Instability
Networks
Percolation
Perturbation methods
Phase transitions
Stability
Triangles
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Summary:Complex networks have been mostly characterized from the point of view of the degree distribution of their nodes and a few other motifs (or modules), with a special attention to triangles and cliques. The most exotic phenomena have been observed when the exponent γ of the associated power-law degree distribution is sufficiently small. In particular, a zero percolation threshold takes place for , and an anomalous critical behavior sets in for . In this letter we prove that in sparse scale-free networks characterized by a cut-off scaling with the sistem size N, relative fluctuations are actually never negligible: given a motif Γ, we analyze the relative fluctuations of the associated density of Γ, and we show that there exists an interval in γ, , where does not go to zero in the thermodynamic limit, where and , and being the smallest and the largest degree of Γ, respectively. Remarkably, in diverges, implying the instability of Γ to small perturbations.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/105/28005