Approximating Personalized Katz Centrality in Dynamic Graphs

Nathan, Eisha; Bader, David A.

doi:10.1007/978-3-319-78024-5_26

Cited by 12 publications

(7 citation statements)

References 17 publications

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“…The number of walks is set to d = 6 by default. The attenuation factor α = 0.85 ∥A ∥ 2 according to the literature [5,30] where ∥A∥ 2 denotes the 2-norm of matrix A. The number of loops is set to l = 20, which is an empirical value from the experiments.…”

Section: Methodsmentioning

confidence: 99%

“…The baseline algorithms we choose to compare with came from the literature [14] by Foster et al and [30] by Nathan et al and therefore we refer them as Foster and Nathan respectively hereinafter:…”

Section: Methodsmentioning

confidence: 99%

“…The algorithm performs well and is widely used in many toolkits for complex network. Furthermore, an algorithm in [30] also uses iterative method to approximate a special personalized variant of Katz centrality with cost of O(km) by computing weighted counts of the number of walks from one vertex to all the vertices in the graph where k is the number of limited walks. Another approximate algorithm [38] is proposed for Katz ranking computation in a special case where α < 1/deg max .…”

Section: Related Work 21 Computation Of Katz Centralitymentioning

confidence: 99%

“…A more efficient approach is to solve a linear system when the system is fairly small by using Cholesky decomposition, which costs O(n 2 ) [31]. Some approximation algorithms [14,30] are developed based on iterative methods that respectively cost O(m + n) and O(km), where k is the number of limited walks, m is the number of edges in the graph and m ∈ O(n 2 ) in the worst case. For large scale network where the number of edges m can also be very large as millions or billions and thus these approximation methods may be still computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

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Sake

Lin

Song

et al. 2021

ACM Trans. Knowl. Discov. Data

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Katz centrality is a fundamental concept to measure the influence of a vertex in a social network. However, existing approaches to calculating Katz centrality in a large-scale network are unpractical and computationally expensive. In this article, we propose a novel method to estimate Katz centrality based on graph sampling techniques, which object to achieve comparable estimation accuracy of the state-of-the-arts with much lower computational complexity. Specifically, we develop a Horvitz–Thompson estimate for Katz centrality by using a multi-round sampling approach and deriving an unbiased mean value estimator. We further propose SAKE , a <underline>S</underline> ampling-based <underline>A</underline> lgorithm for fast <underline>K</underline> atz centrality <underline>E</underline> stimation. We prove that the estimator calculated by SAKE is probabilistically guaranteed to be within an additive error from the exact value. Extensive evaluation experiments based on four real-world networks show that the proposed algorithm can estimate Katz centralities for partial vertices with low sampling rate, low computation time, and it works well in identifying high influence vertices in social networks.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Related Work 21 Computation Of Katz Centralitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sake

Lin

Song

et al. 2021

ACM Trans. Knowl. Discov. Data

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show abstract

“…Their algorithm achieved speedups of over two orders of magnitude over the simple algorithms that perform static recomputation every time the graph changes. Later, they improved their algorithm [182] to handle updates by using an alternative, agglomerative method of calculating Katz scores. While their static algorithm is already several orders of magnitude faster than typical linear algebra approaches, their dynamic algorithm is also faster than pure static recomputation every time the graph changes.…”

Section: Centralitiesmentioning

confidence: 99%

Recent Advances in Fully Dynamic Graph Algorithms

Hanauer¹,

Henzinger²,

Schulz³

2021

Preprint

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In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we survey recent engineering and theory results in the area of fully dynamic graph algorithms.

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Sampling Based Katz Centrality Estimation for Large-Scale Social Networks

Lin

Nguyen

et al. 2020

Lecture Notes in Computer Science

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Approximating Personalized Katz Centrality in Dynamic Graphs

Cited by 12 publications

References 17 publications

Sake

Sake

Recent Advances in Fully Dynamic Graph Algorithms

Sampling Based Katz Centrality Estimation for Large-Scale Social Networks

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