CENTER FOR APPLIED MATHEMATICS AND THEORETICAL PHYSICS

UNIVERZA V MARIBORU UNIVERSITY OF MARIBOR

KREKOVA 2 SI-2000 MARIBOR SLOVENIA

Phone +(386) (2) 2355 350 and 2355 351 Fax +(386) (2) 2355 360

Robnik@uni-mb.si www.camtp.uni-mb.si

PROF.DR. MARKO ROBNIK, DIRECTOR

**Abstract**:
Many of real-world complex networks possess common features
such as the scale-free and small-world properties. Recent studies
reveal that this can be explained by universal origins. Fractal
property of complex networks has been observed in 2005 by Song et al.
Nature 433, 392 (2005). It has not yet been clarified what condition is
required for fractal networks.
We study the relation between fractality, criticality, and the
small-world property by examining two
scale-free network models, the fitness model and the acquaintance network
model. We define the critical point of a network at which the
correlation length assumed to be proportional to the average node-pair
distance diverges. The correlation length and the order
parameter behave critically near the critical point for both models. At the
critical point, the largest network cluster becomes fractal. Above the
critical point, the proportionality coefficient between the correlation
length and the average node-pair distance depends logarithmically on the
number of nodes.
The network is fractal in a shorter length scale than
correlation length and has the small-world property in a longer scale.

**Seminarsko predavanje (v angleškem jeziku)
bo v torek 3. junija 2008 ob 15:15 uri
v seminarski sobi CAMTP na Krekovi 2, pritličje desno.
Vljudno vabljeni vsi zainteresirani, tudi študentje.**

Prof.Dr. Marko Robnik

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