Centrality Analysis for Modified Lattices

Paton, Martin; Akartunalı, Kerem; Higham, Desmond J.

doi:10.1137/17m1114247

Cited by 6 publications

(8 citation statements)

References 27 publications

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“…This is shown in Figure 4 where we plot the PageRank vector of the cycle 100 perturbed with one additional edge that connects nodes 1 and 40, for different values of and for = Γ . Consistently with the analysis carried out in [49], we observe two localized peaks that appear in the PageRank vector s ∞ entries corresponding to the nodes 1 and 40. At the same time, nonlocal versions of PageRank smooth out these peaks as soon as we let the value of decrease.…”

Section: Stability and Nonlocalitysupporting

confidence: 88%

“…most of the measure weight tends to concentrate around few most important nodes while giving to all the other nodes a small and numerically identical value, and thus ranking. This phenomenon has also the secondary effect of producing high variations in the value of the entries of the PageRank vector when the network topology faces a small perturbation, for example few edges are added or removed from the graph [42,49,50].…”

Section: Stability and Nonlocalitymentioning

confidence: 99%

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Nonlocal pagerank

2021

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In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

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Section: Stability and Nonlocalitysupporting

confidence: 88%

Section: Stability and Nonlocalitymentioning

confidence: 99%

Nonlocal pagerank

2021

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“…The last centrality metric which we refer to as k-betweenness ranks nodes according to the number of their direct offspring summed over all generated k-depth BFS trees. We refer the interested reader to Paton et al (2017) for detailed discussion and a numerical analysis of centrality measures. Algorithm 1.…”

Section: Initial Solution Generationmentioning

confidence: 99%

A heuristic approach for the distance-based critical node detection problem in complex networks

Alozie

Arulselvan

Akartunalı

et al. 2021

Journal of the Operational Research Society

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The distance-based critical node problem involves identifying a subset of nodes in a network whose removal minimises a pre-defined distance-based connectivity measure. Having the classical critical node problem as a special case, the distance-based critical node problem is computationally challenging. In this article, we study the distance-based critical node problem from a heuristic algorithm perspective. We consider the distance-based connectivity objective whose goal is to minimise the number of node pairs connected by a path of length at most k, subject to budgetary constraints. We propose a centrality based heuristic which combines a backbone-based crossover procedure to generate good offspring solutions and a centrality-based neighbourhood search to improve the solution. Extensive computational experiments on real-world and synthetic graphs show the effectiveness of the developed heuristic in generating good solutions when compared to exact solution. Our empirical results also provide useful insights for future algorithm development.

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“…The leading eigenvector of the associated transition matrix can suffer the localization phenomenon [28,33,45], i.e., most of the measure weight tends to concentrate around few most important nodes while giving to all the other nodes a small and numerically identical value, and thus ranking. This phenomenon has also the secondary effect of producing high variations in the value of the entries of the PageRank vector when the network topology faces a small perturbation, for example few edges are added or removed from the graph [32,38,39].…”

Section: Stability and Nonlocalitymentioning

confidence: 99%

Nonlocal PageRank

Cipolla,

Durastante,

Tudisco

2020

Preprint

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In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical for spectral rankings taking into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

show abstract

Centrality Analysis for Modified Lattices

Cited by 6 publications

References 27 publications

Nonlocal pagerank

Nonlocal pagerank

A heuristic approach for the distance-based critical node detection problem in complex networks

Nonlocal PageRank

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