FRACTAL NETWORKS ON SIERPINSKI-TYPE POLYGON
Cheng Zeng, Yumei Xue, Meng Zhou
Abstract
In this paper, the evolving networks are created from a series of Sierpinski-type polygon by applying the encoding method in fractal and symbolic dynamical system. Based on the self-similar structures of our networks, we study the cumulative degree distribution, the clustering coefficient and the standardized average path length. The power-law exponent of the cumulative degree distribution is deduced to be [Formula: see text] and the average clustering coefficients have a uniform lower bound [Formula: see text]. Moreover, we find the asymptotic formula of the average path length of our proposed networks. These results show the scale-free and the small-world effects of these networks.
Topics & Concepts
Sierpinski triangleClustering coefficientMathematicsExponentAverage path lengthFractalDegree distributionPolygon (computer graphics)Type (biology)Degree (music)Cluster analysisPath (computing)Distribution (mathematics)Series (stratigraphy)CombinatoricsStatistical physicsComplex networkMathematical analysisShortest path problemStatisticsComputer sciencePhysicsGraphFrame (networking)EcologyPhilosophyPaleontologyLinguisticsProgramming languageAcousticsTelecommunicationsBiologyFractal and DNA sequence analysisComplex Network Analysis TechniquesTopological and Geometric Data Analysis