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^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

3 Citations (Scopus)

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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
DOIs	https://doi.org/10.1016/j.laa.2022.08.022
Publication status	Published - 15 Dec 2022
MoE publication type	A1 Journal article-refereed

Keywords

Centrality measure
Complex network
Katz centrality
Matrix function
Temporal network

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10.1016/j.laa.2022.08.022Licence: CC BY

SCI_Arrigo_etal_Linear_Algebra_and_its_Applicationcs_2022Final published version, 513 KBLicence: CC BY

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 = "Centrality measure, Complex network, Katz centrality, Matrix function, Temporal network",

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

note = "Funding Information: The work of F.A. was supported by fellowship ECF-2018-453 from the Leverhulme Trust.The work of D.J.H. was supported the Engineering and Physical Sciences Research Council Grants EP/P020720/1 and EP/V046527/1.The work of V.N. and R.W. was supported by an Academy of Finland grant (Suomen Akatemian p{\"a}{\"a}t{\"o}s 331240). Publisher Copyright: {\textcopyright} 2022 The Authors",

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

language = "English",

volume = "655",

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journal = "Linear Algebra and Its Applications",

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T1 - Dynamic Katz and related network measures

AU - Arrigo, Francesca

AU - Higham, Desmond J.

AU - Noferini, Vanni

AU - Wood, Ryan

N1 - Funding Information: The work of F.A. was supported by fellowship ECF-2018-453 from the Leverhulme Trust.The work of D.J.H. was supported the Engineering and Physical Sciences Research Council Grants EP/P020720/1 and EP/V046527/1.The work of V.N. and R.W. was supported by an Academy of Finland grant (Suomen Akatemian päätös 331240). Publisher Copyright: © 2022 The Authors

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 - Centrality measure

KW - Complex network

KW - Katz centrality

KW - Matrix function

KW - Temporal network

UR - http://www.scopus.com/inward/record.url?scp=85138473141&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2022.08.022

DO - 10.1016/j.laa.2022.08.022

M3 - Article

AN - SCOPUS:85138473141

SN - 1873-1856

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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Noferini_Vanni_AoF_Project: Noferini Vanni Academy Project

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Dynamic Katz and related network measures

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Keywords

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Noferini_Vanni_AoF_Project: Noferini Vanni Academy Project

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