Joint estimation of preferential attachment and node fitness in growing complex networks

Pham, Thong; Sheridan, Paul; Shimodaira, Hidetoshi

doi:10.1038/srep32558

Cited by 58 publications

(111 citation statements)

References 60 publications

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“…where C(e) is the set of edges indistinguishable from e. We finally compute the correlation between τ * (e) and the ground truth, using Eq. (16). The resulting bound corresponds to the correlation we would have obtained had we known the true arrival time of edges, without the labeling of G.…”

Section: Inference On Artificial Treesmentioning

confidence: 86%

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Phase Transition in the Recoverability of Network History

et al. 2019

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Network growth processes can be understood as generative models of the structure and history of complex networks. This point of view naturally leads to the problem of network archaeology: reconstructing all the past states of a network from its structure-a difficult permutation inference problem. In this paper, we introduce a Bayesian formulation of network archaeology, with a generalization of preferential attachment as our generative mechanism. We develop a sequential Monte Carlo algorithm to evaluate the posterior averages of this model, as well as an efficient heuristic that uncovers a history well correlated with the true one, in polynomial time. We use these methods to identify and characterize a phase transition in the quality of the reconstructed history, when they are applied to artificial networks generated by the model itself. Despite the existence of a no-recovery phase, we find that nontrivial inference is possible in a large portion of the parameter space as well as on empirical data.

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Section: Inference On Artificial Treesmentioning

confidence: 86%

“…At the level of detailed mechanisms, they have been shown to act effectively as generative models of complex networks [12,13], i.e., as stochastic processes that can explain the minutia of a network's growth [14,15]. This point of view has led, for example, to powerful statistical tests that can help determine how networks evolve and change [16,17].…”

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confidence: 99%

Phase Transition in the Recoverability of Network History

et al. 2019

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“…Equation 1 has a number of applications. Based on the functional forms of A k and η i , we can test for the presence of one and/or the other of the "rich-get-richer" and "fit-getricher" phenomena in a temporal network (Pham, Sheridan, and Shimodaira 2016). These two mechanisms have been advanced to explain another phenomenon called the "generalized friendship paradox" (Feld 1991;Eom and Jo 2014;Momeni and Rabbat 2015).…”

Section: Introductionmentioning

confidence: 99%

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

Pham¹,

Sheridan²,

Shimodaira³

2020

J. Stat. Soft.

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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.

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“…This model shall be compared to the physics-inspired predictive model developed by Wang, Song, and Barabasi [16]. Pham, Sheridan, and Shimodaira [36,37] developed a software package based on this model and demonstrated that it is a valid predictive tool. This model includes three paper-specific parameters: fitness η, immediacy µ, and σ.…”

Section: Discussionmentioning

confidence: 99%