Issue |
EPL
Volume 105, Number 2, January 2014
|
|
---|---|---|
Article Number | 28005 | |
Number of page(s) | 6 | |
Section | Interdisciplinary Physics and Related Areas of Science and Technology | |
DOI | https://doi.org/10.1209/0295-5075/105/28005 | |
Published online | 12 February 2014 |
Fluctuations of motifs and non–self-averaging in complex networks: A self- vs. non–self-averaging phase transition scenario
Cooperative Association for Internet Data Analysis, San Diego Supercomputer Center, UCSD San Diego, CA, USA
Received: 14 September 2013
Accepted: 17 January 2014
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.
PACS: 89.75.Fb – Structures and organization in complex systems / 89.75.Hc – Networks and genealogical trees / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EPLA, 2014
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