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PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks.

Pham T, Sheridan P, Shimodaira H - PLoS ONE (2015)

Bottom Line: We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations.What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form.Independent of our main work, we provide a correction to a consequential error in Newman's original method which had evidently gone unnoticed since its publication over a decade ago.

View Article: PubMed Central - PubMed

Affiliation: Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Osaka, Japan.

ABSTRACT
Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman's original method which had evidently gone unnoticed since its publication over a decade ago.

No MeSH data available.


Related in: MedlinePlus

Comparison between five methods in average relative error.A: B = 100. B: B = 20. See Table 2 for the details of the true attachment kernels Ak used here.
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pone.0137796.g002: Comparison between five methods in average relative error.A: B = 100. B: B = 20. See Table 2 for the details of the true attachment kernels Ak used here.

Mentions: The result is shown in Fig 2. Overall, PAFit with regularization outperformed all remaining methods. This suggests that a small amount of regularization is indeed needed to reduce the error in the estimated result. We also notice that binning helps reduced the error in all methods. The fewer number of bins we used, the better the estimated result was found to be.


PAFit: A Statistical Method for Measuring Preferential Attachment in Temporal Complex Networks.

Pham T, Sheridan P, Shimodaira H - PLoS ONE (2015)

Comparison between five methods in average relative error.A: B = 100. B: B = 20. See Table 2 for the details of the true attachment kernels Ak used here.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4574777&req=5

pone.0137796.g002: Comparison between five methods in average relative error.A: B = 100. B: B = 20. See Table 2 for the details of the true attachment kernels Ak used here.
Mentions: The result is shown in Fig 2. Overall, PAFit with regularization outperformed all remaining methods. This suggests that a small amount of regularization is indeed needed to reduce the error in the estimated result. We also notice that binning helps reduced the error in all methods. The fewer number of bins we used, the better the estimated result was found to be.

Bottom Line: We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations.What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form.Independent of our main work, we provide a correction to a consequential error in Newman's original method which had evidently gone unnoticed since its publication over a decade ago.

View Article: PubMed Central - PubMed

Affiliation: Division of Mathematical Science, Graduate School of Engineering Science, Osaka University, Osaka, Japan.

ABSTRACT
Preferential attachment is a stochastic process that has been proposed to explain certain topological features characteristic of complex networks from diverse domains. The systematic investigation of preferential attachment is an important area of research in network science, not only for the theoretical matter of verifying whether this hypothesized process is operative in real-world networks, but also for the practical insights that follow from knowledge of its functional form. Here we describe a maximum likelihood based estimation method for the measurement of preferential attachment in temporal complex networks. We call the method PAFit, and implement it in an R package of the same name. PAFit constitutes an advance over previous methods primarily because we based it on a nonparametric statistical framework that enables attachment kernel estimation free of any assumptions about its functional form. We show this results in PAFit outperforming the popular methods of Jeong and Newman in Monte Carlo simulations. What is more, we found that the application of PAFit to a publically available Flickr social network dataset yielded clear evidence for a deviation of the attachment kernel from the popularly assumed log-linear form. Independent of our main work, we provide a correction to a consequential error in Newman's original method which had evidently gone unnoticed since its publication over a decade ago.

No MeSH data available.


Related in: MedlinePlus