Dynamic Katz and related network measures

Francesca Arrigo; Desmond J. Higham; Vanni  Noferini; Ryan Wood

doi:10.1016/j.laa.2022.08.022

Dynamic Katz and related network measures

Francesca Arrigo, Desmond J. Higham, Vanni Noferini, Ryan Wood

Mathematics And Statistics

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Abstract

We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.

Original language	English
Pages (from-to)	159-185
Number of pages	27
Journal	Linear Algebra and its Applications
Volume	655
Early online date	28 Aug 2022
DOIs	https://doi.org/10.1016/j.laa.2022.08.022
Publication status	Published - 15 Dec 2022

Keywords

complex network
matrix function
centrality measures
temporal network
Katz centrality

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10.1016/j.laa.2022.08.022Licence: CC BY 4.0

Arrigo-etal-LAA-2022-Dynamic-Katz-and-related-network-measuresFinal published version, 512 KBLicence: CC BY 4.0

Don't look back -- non-backtracking walks in complex networks (ECF)
Arrigo, F.
Leverhulme Trust
1/05/19 → 30/04/22
Project: Research Fellowship

Cite this

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title = "Dynamic Katz and related network measures",

abstract = "We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.",

keywords = "complex network, matrix function, centrality measures, temporal network, Katz centrality",

author = "Francesca Arrigo and Higham, {Desmond J.} and Vanni Noferini and Ryan Wood",

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doi = "10.1016/j.laa.2022.08.022",

language = "English",

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T1 - Dynamic Katz and related network measures

AU - Arrigo, Francesca

AU - Higham, Desmond J.

AU - Noferini, Vanni

AU - Wood, Ryan

PY - 2022/12/15

Y1 - 2022/12/15

N2 - We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.

AB - We study walk-based centrality measures for time-ordered network sequences. For the case of standard dynamic walk-counting, we show how to derive and compute centrality measures induced by analytic functions. We also prove that dynamic Katz centrality, based on the resolvent function, has the unique advantage of allowing computations to be performed entirely at the node level. We then consider two distinct types of backtracking and develop a framework for capturing dynamic walk combinatorics when either or both is disallowed.

KW - complex network

KW - matrix function

KW - centrality measures

KW - temporal network

KW - Katz centrality

U2 - 10.1016/j.laa.2022.08.022

DO - 10.1016/j.laa.2022.08.022

M3 - Article

SN - 0024-3795

VL - 655

SP - 159

EP - 185

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Dynamic Katz and related network measures

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Keywords

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Projects

Don't look back -- non-backtracking walks in complex networks (ECF)

Cite this