Fluctuations of motifs and non–self-averaging in complex networks: A self- vs. non–self-averaging phase transition scenario
- M. Ostilli
DOIAbstract
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 $\gamma<3$ , and an anomalous critical behavior sets in for $\gamma<5$ . 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 $R_{\Gamma}$ of the associated density of Γ, and we sh...
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