Thong Pham

selected publications

1. Non-parametric Estimation of the Preferential Attachment Function from One Network Snapshot

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   Journal of Complex Networks, Sep 2021

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   Preferential attachment is commonly invoked to explain the emergence of those heavy-tailed degree distributions characteristic of growing network representations of diverse real-world phenomena. Experimentally confirming this hypothesis in real-world growing networks is an important frontier in network science research. Conventional preferential attachment estimation methods require that a growing network be observed across at least two snapshots in time. Numerous publicly available growing network datasets are, however, only available as single snapshots, leaving the applied network scientist with no means of measuring preferential attachment in these cases. We propose a nonparametric method, called PAFit-oneshot, for estimating preferential attachment in a growing network from one snapshot. PAFit-oneshot corrects for a previously unnoticed bias that arises when estimating preferential attachment values only for degrees observed in the single snapshot. Our work provides a means of measuring preferential attachment in a large number of publicly available one-snapshot networks. As a demonstration, we estimated preferential attachment in three such networks, and found sublinear preferential attachment in all cases. PAFit-oneshot is implemented in the R package PAFit.

   @article{pham_2021,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     title = {Non-parametric Estimation of the Preferential Attachment Function from One Network Snapshot},
     journal = {Journal of Complex Networks},
     volume = {9},
     number = {5},
     year = {2021},
     month = sep,
     issn = {2051-1329},
     doi = {10.1093/comnet/cnab024},
     url = {https://doi.org/10.1093/comnet/cnab024},
     note = {cnab024},
     eprint = {https://academic.oup.com/comnet/article-pdf/9/5/cnab024/40830667/cnab024.pdf}
   }

2. PAFit: An R Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   Journal of Statistical Software, Feb 2020

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   Many real-world systems are profitably described as complex networks that grow over time. Preferential attachment and node fitness are two simple growth mechanisms that not only explain certain structural properties commonly observed in real-world systems, but are also tied to a number of applications in modeling and inference. While there are statistical packages for estimating various parametric forms of the preferential attachment function, there is no such package implementing non-parametric estimation procedures. The non-parametric approach to the estimation of the preferential attachment function allows for comparatively finer-grained investigations of the "rich-get-richer" phenomenon that could lead to novel insights in the search to explain certain nonstandard structural properties observed in real-world networks. This paper introduces the R package PAFit, which implements non-parametric procedures for estimating the preferential attachment function and node fitnesses in a growing network, as well as a number of functions for generating complex networks from these two mechanisms. The main computational part of the package is implemented in C++ with OpenMP to ensure scalability to large-scale networks. In this paper, we first introduce the main functionalities of PAFit through simulated examples, and then use the package to analyze a collaboration network between scientists in the field of complex networks. The results indicate the joint presence of "richget-richer" and "fit-get-richer" phenomena in the collaboration network. The estimated attachment function is observed to be near-linear, which we interpret as meaning that the chance an author gets a new collaborator is proportional to their current number of collaborators. Furthermore, the estimated author fitnesses reveal a host of familiar faces from the complex networks community among the field’s topmost fittest network scientists.

   @article{pham_2020,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     title = {{PAFit}: An {R} Package for the Non-Parametric Estimation of Preferential Attachment and Node Fitness in Temporal Complex Networks},
     journal = {Journal of Statistical Software},
     volume = {92},
     number = {3},
     year = {2020},
     month = feb,
     keywords = {temporal networks; dynamic networks; preferential attachment; fitness; rich-get-richer; fit-get-richer; R; C++; Rcpp; OpenMP},
     issn = {1548-7660},
     pages = {1--30},
     doi = {10.18637/jss.v092.i03},
     url = {https://www.jstatsoft.org/v092/i03}
   }

3. Joint Estimation of Preferential Attachment and Node Fitness in Growing Complex Networks

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   Scientific Reports, Sep 2016

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   Complex network growth across diverse fields of science is hypothesized to be driven in the main by a combination of preferential attachment and node fitness processes. For measuring the respective influences of these processes, previous approaches make strong and untested assumptions on the functional forms of either the preferential attachment function or fitness function or both. We introduce a Bayesian statistical method called PAFit to estimate preferential attachment and node fitness without imposing such functional constraints that works by maximizing a log-likelihood function with suitably added regularization terms. We use PAFit to investigate the interplay between preferential attachment and node fitness processes in a Facebook wall-post network. While we uncover evidence for both preferential attachment and node fitness, thus validating the hypothesis that these processes together drive complex network evolution, we also find that node fitness plays the bigger role in determining the degree of a node. This is the first validation of its kind on real-world network data. But surprisingly the rate of preferential attachment is found to deviate from the conventional log-linear form when node fitness is taken into account. The proposed method is implemented in the R package PAFit.

   @article{pham_2016,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     title = {Joint Estimation of Preferential Attachment and Node Fitness in Growing Complex Networks},
     journal = {Scientific Reports},
     year = {2016},
     month = sep,
     volume = {6},
     page = {32558},
     url = {http://dx.doi.org/10.1038/srep32558},
     doi = {10.1038/srep32558},
     publisher = {Nature Publishing Group}
   }

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

   Pham, Thong, Sheridan, Paul, and Shimodaira, Hidetoshi

   PLOS ONE, Sep 2015

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   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.

   @article{pham_2015,
     author = {Pham, Thong and Sheridan, Paul and Shimodaira, Hidetoshi},
     journal = {PLOS ONE},
     title = {{PAFit}: A Statistical Method for Measuring Preferential
     Attachment in Temporal Complex Networks},
     year = {2015},
     month = sep,
     volume = {10},
     pages = {e0137796},
     number = {9},
     publisher = {Public Library of Science},
     doi = {10.1371/journal.pone.0137796},
     url = {http://dx.doi.org/10.1371/journal.pone.0137796}
   }