| Author | Title | Year | Journal/Proceedings | Reftype | DOI/URL |
|---|---|---|---|---|---|
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-Law Distributions in Empirical Data [BibTeX] |
2009 | SIAM Review Vol. 51(4), pp. 661-703 |
article | DOI URL |
BibTeX:
@article{clauset2009powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-Law Distributions in Empirical Data},
journal = {SIAM Review},
year = {2009},
volume = {51},
number = {4},
pages = {661-703},
url = {/brokenurl# http://dx.doi.org/10.1137/070710111 },
doi = {http://dx.doi.org/10.1137/070710111}
}
|
|||||
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-Law Distributions in Empirical Data | 2009 | SIAM Review Vol. 51(4), pp. 661-703 |
article | DOI URL |
| Abstract: Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out. | |||||
BibTeX:
@article{clauset2009powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-Law Distributions in Empirical Data},
journal = {SIAM Review},
publisher = {SIAM},
year = {2009},
volume = {51},
number = {4},
pages = {661--703},
url = {http://link.aip.org/link/?SIR/51/661/1},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
|||||
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-Law Distributions in Empirical Data | 2009 | SIAM Review Vol. 51(4), pp. 661-703 |
article | DOI URL |
| Abstract: Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out. | |||||
BibTeX:
@article{clauset2009powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-Law Distributions in Empirical Data},
journal = {SIAM Review},
publisher = {SIAM},
year = {2009},
volume = {51},
number = {4},
pages = {661--703},
url = {http://link.aip.org/link/?SIR/51/661/1},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
|||||
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-law distributions in empirical data | 2007 | misc | DOI URL | |
| Abstract: Power-law distributions occur in many situations of scientific interest and ve significant consequences for our understanding of natural and man-made enomena. Unfortunately, the detection and characterization of power laws is mplicated by the large fluctuations that occur in the tail of the stribution -- the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power-law behavior lds. Commonly used methods for analyzing power-law data, such as ast-squares fitting, can produce substantially inaccurate estimates of rameters for power-law distributions, and even in cases where such methods turn accurate answers they are still unsatisfactory because they give no dication of whether the data obey a power law at all. Here we present a incipled statistical framework for discerning and quantifying power-law havior in empirical data. Our approach combines maximum-likelihood fitting thods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic d likelihood ratios. We evaluate the effectiveness of the approach with tests synthetic data and give critical comparisons to previous approaches. We also ply the proposed methods to twenty-four real-world data sets from a range of fferent disciplines, each of which has been conjectured to follow a power-law stribution. In some cases we find these conjectures to be consistent with the ta while in others the power law is ruled out. |
|||||
BibTeX:
@misc{clauset2007powerlaw,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-law distributions in empirical data},
year = {2007},
note = {cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/},
url = {http://arxiv.org/abs/0706.1062},
doi = {http://dx.doi.org/10.1137/070710111}
}
|
|||||
| Clauset, A., Shalizi, C.R. & Newman, M.E.J. | Power-law distributions in empirical data | 2007 | misc | URL | |
| Abstract: Power-law distributions occur in many situations of scientific interest and
ve significant consequences for our understanding of natural and man-made enomena. Unfortunately, the detection and characterization of power laws is mplicated by the large fluctuations that occur in the tail of the stribution -- the part of the distribution representing large but rare events and by the difficulty of identifying the range over which power-law behavior lds. Commonly used methods for analyzing power-law data, such as ast-squares fitting, can produce substantially inaccurate estimates of rameters for power-law distributions, and even in cases where such methods turn accurate answers they are still unsatisfactory because they give no dication of whether the data obey a power law at all. Here we present a incipled statistical framework for discerning and quantifying power-law havior in empirical data. Our approach combines maximum-likelihood fitting thods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic d likelihood ratios. We evaluate the effectiveness of the approach with tests synthetic data and give critical comparisons to previous approaches. We also ply the proposed methods to twenty-four real-world data sets from a range of fferent disciplines, each of which has been conjectured to follow a power-law stribution. In some cases we find these conjectures to be consistent with the ta while in others the power law is ruled out. |
|||||
BibTeX:
@misc{Clauset2007,
author = {Clauset, Aaron and Shalizi, Cosma Rohilla and Newman, M. E. J.},
title = {Power-law distributions in empirical data},
year = {2007},
note = {cite arxiv:0706.1062
|
|||||
| Clauset, A., Newman, M.E.J. & Moore, C. | Finding community structure in very large networks | 2004 | Physical Review E, pp. 1- 6 | article | DOI |
| Abstract: Abstract: The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(mdlog n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m n and d log n, in which case our algorithm runs in essentially linear time, O(n log2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers. | |||||
BibTeX:
@article{clauset2004,
author = {Clauset, Aaron and Newman, M. E. J. and and Cristopher Moore},
title = {Finding community structure in very large networks},
journal = {Physical Review E},
year = {2004},
pages = {1-- 6},
doi = {http://dx.doi.org/10.1103/PhysRevE.70.066111}
}
|
|||||
| Clauset, A., Newman, M.E.J. & Moore, C. | Finding community structure in very large networks [BibTeX] |
2004 | Physical Review E Vol. 70, pp. 066111 |
article | URL |
BibTeX:
@article{clauset-2004-70,
author = {Clauset, Aaron and Newman, M. E. J. and Moore, Cristopher},
title = {Finding community structure in very large networks},
journal = {Physical Review E},
year = {2004},
volume = {70},
pages = {066111},
url = {http://www.citebase.org/abstract?id=oai:arXiv.org:cond-mat/0408187}
}
|
|||||
| Clauset, A., Newman, M. & Moore, C. | Finding community structure in very large networks [BibTeX] |
2004 | Physical Review E Vol. 70, pp. 066111 |
article | URL |
BibTeX:
@article{clauset-2004-70,
author = {Clauset, Aaron and Newman, M.E.J. and Moore, Cristopher},
title = {Finding community structure in very large networks},
journal = {Physical Review E},
year = {2004},
volume = {70},
pages = {066111},
url = {http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:cond-mat/0408187}
}
|
|||||
| Clauset, A., Newman, M.E.J. & Moore, C. | Finding community structure in very large networks | 2004 | misc | URL | |
| Abstract: The discovery and analysis of community structure in networks is a topic of
nsiderable recent interest within the physics community, but most methods oposed so far are unsuitable for very large networks because of their mputational cost. Here we present a hierarchical agglomeration algorithm for tecting community structure which is faster than many competing algorithms: s running time on a network with n vertices and m edges is O(m d log n) where is the depth of the dendrogram describing the community structure. Many al-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in ich case our algorithm runs in essentially linear time, O(n log^2 n). As an ample of the application of this algorithm we use it to analyze a network of ems for sale on the web-site of a large online retailer, items in the network ing linked if they are frequently purchased by the same buyer. The network s more than 400,000 vertices and 2 million edges. We show that our algorithm n extract meaningful communities from this network, revealing large-scale tterns present in the purchasing habits of customers. |
|||||
BibTeX:
@misc{citeulike:95936,
author = {Clauset, Aaron and Newman, M. E. J. and Moore, Cristopher},
title = {Finding community structure in very large networks},
year = {2004},
url = {http://arxiv.org/abs/cond-mat/0408187}
}
|
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