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.