Complex networks: A mixture of power-law and Weibull distributions Export

@article{citeulike:5707206, abstract = {Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected, unweighted networks into two types: p2c and p2p. The p2c edge represents a hierarchical relationship between two nodes, while the p2p edge represents an equal relationship between two nodes. It is surprising and unexpected that for many real-world networks from a wide variety of domains (including computer science, transportation, biology, engineering and social science etc), the p2c degree distribution follows a power law more strictly than the total degree distribution, while the p2p degree distribution follows the Weibull distribution very well. Thus, the total degree distribution can be seen as a mixture of power-law and Weibull distributions. More surprisingly, it is found that in many cases, the total degree distribution can be better described by the Weibull distribution, rather than a power law as previously suggested. By comparing two topology models, we think that the origin of the Weibull distribution in complex networks might be a mixture of both preferential and random attachments when networks evolve.}, archivePrefix = {arXiv}, author = {Xu, Ke and Liu, Liandong and Liang, Xiao}, citeulike-article-id = {5707206}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.0588}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.0588}, day = {1}, eprint = {0908.0588}, keywords = {characterization, modelling, networks, power-law}, month = {Sep}, posted-at = {2009-09-02 16:52:56}, priority = {2}, title = {Complex networks: A mixture of power-law and Weibull distributions}, url = {http://arxiv.org/abs/0908.0588}, year = {2009} }

TY - JOUR ID - citeulike:5707206 L3 - citeulike-article-id:5707206 N2 - Complex networks have recently aroused a lot of interest. However, network edges are considered to be the same in almost all these studies. In this paper, we present a simple classification method, which divides the edges of undirected, unweighted networks into two types: p2c and p2p. The p2c edge represents a hierarchical relationship between two nodes, while the p2p edge represents an equal relationship between two nodes. It is surprising and unexpected that for many real-world networks from a wide variety of domains (including computer science, transportation, biology, engineering and social science etc), the p2c degree distribution follows a power law more strictly than the total degree distribution, while the p2p degree distribution follows the Weibull distribution very well. Thus, the total degree distribution can be seen as a mixture of power-law and Weibull distributions. More surprisingly, it is found that in many cases, the total degree distribution can be better described by the Weibull distribution, rather than a power law as previously suggested. By comparing two topology models, we think that the origin of the Weibull distribution in complex networks might be a mixture of both preferential and random attachments when networks evolve. TI - Complex networks: A mixture of power-law and Weibull distributions KW - characterization KW - modelling KW - networks KW - power-law AU - Xu, Ke AU - Liu, Liandong AU - Liang, Xiao PY - 2009/Sep/01/ UR - http://arxiv.org/abs/0908.0588 ER -