Open AccessPosted Content
Consistent Estimation in General Sublinear Preferential Attachment Trees
TL;DR: In this paper, an empirical estimator of the preferential attachment function in the setting of general preferential attachment trees is proposed, which is based on a supercritical continuous-time branching process framework.
read more
Abstract: We propose an empirical estimator of the preferential attachment function $f$ in the setting of general preferential attachment trees. Using a supercritical continuous-time branching process framework, we prove the almost sure consistency of the proposed estimator. We perform simulations to study the empirical properties of our estimators.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Inference on the History of a Randomly Growing Tree
Harry Crane,Min Xu +1 more
TL;DR: This work considers the problem of statistical inference on aspects of the latent history of a randomly growing tree using only a single snapshot of the final tree, and proposes algorithms for constructing confidence sets with valid frequentist coverage as well as bounds on the expected size of the confidence sets.
3
•Proceedings Article
The Buckley-Osthus model and the block preferential attachment model: statistical analysis and application
Wenpin Tang,Xin Guo,Fengmin Tang +2 more
- 12 Jul 2020
TL;DR: It is proved that the maximum likelihood estimates for both models are consistent and this paper applies both models to study the evolution of a real-world network.
3
•Posted Content
Consistency of the Buckley-Osthus model and the hierarchical preferential attachment model.
Xin Guo,Fengmin Tang,Wenpin Tang +2 more
TL;DR: It is proved that the maximum likelihood estimates for both models are consistent and this paper applies both models to study the evolution of a real-world network.
On the asymptotic normality of estimating the affine preferential attachment network models with random initial degrees
Fengnan Gao,Aad van der Vaart +1 more
TL;DR: In this paper, the affine parameter and power-law exponent in the preferential attachment model with random initial degrees were derived and a quasi-maximum likelihood estimator was proposed to overcome the dependence on the history of the initial degrees.
•Posted Content
Consistency of Hill Estimators in a Linear Preferential Attachment Model
Tiandong Wang,Sidney I. Resnick +1 more
TL;DR: In this paper, the authors show the convergence of the tail empirical measure, from which the consistency of the Hill estimators is obtained and give a proof for a particular linear preferential attachment model and use simulation results as an illustration in other choices of models.
References
Emergence of Scaling in Random Networks
TL;DR: A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.
39.1K
Mean-field theory for scale-free random networks
TL;DR: A mean-field method is developed to predict the growth dynamics of the individual vertices of the scale-free model, and this is used to calculate analytically the connectivity distribution and the scaling exponents.
Scale-free characteristics of random networks: the topology of the world-wide web
TL;DR: This work introduces a model that leads to a scale-free network, capturing in a minimal fashion the self-organization processes governing the world-wide web.
Random Graphs and Complex Networks
Remco van der Hofstad
- 01 Jan 2017
TL;DR: This chapter explains why many real-world networks are small worlds and have large fluctuations in their degrees, and why Probability theory offers a highly effective way to deal with the complexity of networks, and leads us to consider random graphs.
Organization of growing random networks
Pavel L. Krapivsky,Sidney Redner +1 more
TL;DR: The organizational development of growing random networks is investigated, and the combined age and degree distribution of nodes shows that old nodes typically have a large degree.