Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system’s dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.
REFERENCES
1.
S.
Boccaletti
, V.
Latora
, Y.
Moreno
, M.
Chavez
, and D.-U.
Hwang
, “Complex networks: Structure and dynamics
,” Phys. Rep.
424
, 175
–308
(2006
). 2.
A.
Arenas
, A.
Díaz-Guilera
, J.
Kurths
, Y.
Moreno
, and C.
Zhou
, “Synchronization in complex networks
,” Phys. Rep.
469
, 93
–153
(2008
). 3.
E.
Bullmore
and O.
Sporns
, “Complex brain networks: Graph theoretical analysis of structural and functional systems
,” Nat. Rev. Neurosci.
10
, 186
–198
(2009
). 4.
J. F.
Donges
, Y.
Zou
, N.
Marwan
, and J.
Kurths
, “The backbone of the climate network
,” Europhys. Lett.
87
, 48007
(2009
). 5.
R. J.
Allen
and T. C.
Elston
, “From physics to pharmacology?
,” Rep. Prog. Phys.
74
, 016601
(2011
). 6.
M.
Barthélemy
, “Spatial networks
,” Phys. Rep.
499
, 1
–101
(2011
). 7.
A.-L.
Barabási
, N.
Gulbahce
, and J.
Loscalzo
, “Network medicine: A network-based approach to human disease
,” Nat. Rev. Genet.
12
, 56
–68
(2011
). 8.
M. E. J.
Newman
, “Communities, modules and large-scale structure in networks
,” Nat. Phys.
8
, 25
–31
(2012
). 9.
A.
Baronchelli
, R.
Ferrer-i-Cancho
, R.
Pastor-Satorras
, N.
Chater
, and M. H.
Christiansen
, “Networks in cognitive science
,” Trends Cogn. Sci.
17
, 348
–360
(2013
). 10.
K.
Lehnertz
, G.
Ansmann
, S.
Bialonski
, H.
Dickten
, C.
Geier
, and S.
Porz
, “Evolving networks in the human epileptic brain
,” Physica D
267
, 7
–15
(2014
). 11.
T.
Heckmann
, W.
Schwanghart
, and J. D.
Phillips
, “Graph theory—Recent developments of its application in geomorphology
,” Geomorphology
243
, 130
–146
(2015
). 12.
J.
Gao
, B.
Barzel
, and A.-L.
Barabási
, “Universal resilience patterns in complex networks
,” Nature
530
, 307
(2016
). 13.
J. F.
Donges
, Y.
Zou
, N.
Marwan
, and J.
Kurths
, “Complex networks in climate dynamics
,” Eur. Phys. J. Spec. Top.
174
, 157
–179
(2009
). 14.
D.
Zhou
, A.
Gozolchiani
, Y.
Ashkenazy
, and S.
Havlin
, “Teleconnection paths via climate network direct link detection
,” Phys. Rev. Lett.
115
, 268501
(2015
). 15.
P.
Uetz
, L.
Giot
, G.
Cagney
, T. A.
Mansfield
, R. S.
Judson
, J. R.
Knight
, D.
Lockshon
, V.
Narayan
, M.
Srinivasan
, P.
Pochart
, A.
Qureshi-Emili
, Y.
Li
, B.
Godwin
, D.
Conover
, T.
Kalbfleisch
, G.
Vijayadamodar
, M.
Yang
, M.
Johnston
, S.
Fields
, and J. M.
Rothberg
, “A comprehensive analysis of protein–protein interactions in Saccharomyces cerevisiae
,” Nature
403
, 623
–627
(2000
). 16.
A. L.
Tyler
, F. W.
Asselbergs
, S. M.
Williams
, and J. H.
Moore
, “Shadows of complexity: What biological networks reveal about epistasis and pleiotropy
,” BioEssays
31
, 220
–227
(2009
). 17.
S. J.
Hegland
, A.
Nielsen
, A.
Lázaro
, A.-L.
Bjerknes
, and Ø.
Totland
, “How does climate warming affect plant-pollinator interactions?
,” Ecol. Lett.
12
, 184
–195
(2009
). 18.
J. M.
Olesen
, J.
Bascompte
, Y. L.
Dupont
, H.
Elberling
, C.
Rasmussen
, and P.
Jordano
, “Missing and forbidden links in mutualistic networks
,” Proc. Roy. Soc. B: Biol. Sci.
278
, 725
–732
(2011
). 19.
L.
Halekotte
and U.
Feudel
, “Minimal fatal shocks in multistable complex networks
,” Sci. Rep.
10
, 11783
(2020
). 20.
E.
Delmas
, M.
Besson
, M.-H.
Brice
, L. A.
Burkle
, G. V.
Dalla Riva
, M.-J.
Fortin
, D.
Gravel
, P. R.
Guimarães
, Jr., D. H.
Hembry
, E. A.
Newman
, J. M.
Olesen
, M. M.
Pires
, J. D.
Yeakel
, and T.
Poisot
, “Analysing ecological networks of species interactions
,” Biol. Rev.
94
, 16
–36
(2019
). 21.
J. P.
Onnela
, J.
Saramäki
, J.
Hyvönen
, G.
Szábo
, D.
Lazer
, K.
Kaski
, J.
Kertész
, and A.-L.
Barabási
, “Structure and tie strengths in mobile communication networks
,” Proc. Natl. Acad. Sci. U.S.A.
104
, 7332
–7336
(2007
). 22.
G.
Palla
, A.-L.
Barabási
, and T.
Vicsek
, “Quantifying social group evolution
,” Nature
446
, 664
–667
(2007
). 23.
S.
Bialonski
, M.
Horstmann
, and K.
Lehnertz
, “From brain to earth and climate systems: Small-world interaction networks or not?
,” Chaos
20
, 013134
(2010
). 24.
J.
Hlinka
, D.
Hartman
, and M.
Paluš
, “Small-world topology of functional connectivity in randomly connected dynamical systems
,” Chaos
22
, 033107
(2012
). 25.
S.
Porz
, M.
Kiel
, and K.
Lehnertz
, “Can spurious indications for phase synchronization due to superimposed signals be avoided?
,” Chaos
24
, 033112
(2014
). 26.
V.
Wens
, “Investigating complex networks with inverse models: Analytical aspects of spatial leakage and connectivity estimation
,” Phys. Rev. E
91
, 012823
(2015
). 27.
M. T.
Gastner
and G.
Ódor
, “The topology of large open connectome networks for the human brain
,” Sci. Rep.
6
, 27249
(2016
). 28.
D.
Papo
, M.
Zanin
, J. H.
Martínez
, and J. M.
Buldú
, “Beware of the small-world neuroscientist!
,” Front. Hum. Neurosci.
10
, 96
(2016
). 29.
J.
Hlinka
, D.
Hartman
, N.
Jajcay
, D.
Tomeček
, J.
Tintěra
, and M.
Paluš
, “Small-world bias of correlation networks: From brain to climate
,” Chaos
27
, 035812
(2017
). 30.
M.
Zanin
, S.
Belkoura
, J.
Gomez
, C.
Alfaro
, and J.
Cano
, “Topological structures are consistently overestimated in functional complex networks
,” Sci. Rep.
8
, 11980
(2018
). 31.
S.
Bialonski
, M.
Wendler
, and K.
Lehnertz
, “Unraveling spurious properties of interaction networks with tailored random networks
,” PLoS One
6
, e22826
(2011
). 32.
N. N.
Chung
, L. Y.
Chew
, J.
Zhou
, and C. H.
Lai
, “Impact of edge removal on the centrality betweenness of the best spreaders
,” Europhys. Lett.
98
, 58004
(2012
). 33.
L.
Lü
and T.
Zhou
, “Link prediction in complex networks: A survey
,” Physica A
390
, 1150
–1170
(2011
). 34.
L.
Lü
, L.
Pan
, T.
Zhou
, Y.-C.
Zhang
, and H. E.
Stanley
, “Toward link predictability of complex networks
,” Proc. Natl. Acad. Sci. U.S.A.
112
, 2325
–2330
(2015
). 35.
H.
Liao
, M. S.
Mariani
, M.
Medo
, Y.-C.
Zhang
, and M.-Y.
Zhou
, “Ranking in evolving complex networks
,” Phys. Rep.
689
, 1
–54
(2017
). 36.
M. A.
Kramer
, U. T.
Eden
, S. S.
Cash
, and E. D.
Kolaczyk
, “Network inference with confidence from multivariate time series
,” Phys. Rev. E
79
, 061916
(2009
). 37.
X.
Yan
, L. G. S.
Jeub
, A.
Flammini
, F.
Radicchi
, and S.
Fortunato
, “Weight thresholding on complex networks
,” Phys. Rev. E
98
, 042304
(2018
). 38.
A.
Zeng
and G.
Cimini
, “Removing spurious interactions in complex networks
,” Phys. Rev. E
85
, 036101
(2012
). 39.
Q.
Zhang
, M.
Li
, and Y.
Deng
, “Measure the structure similarity of nodes in complex networks based on relative entropy
,” Physica A
491
, 749
–763
(2018
). 40.
A.
Kumar
, S. S.
Singh
, K.
Singh
, and B.
Biswas
, “Link prediction techniques, applications, and performance: A survey
,” Physica A
553
, 124289
(2020
). 41.
G. T.
Cantwell
, Y.
Liu
, B. F.
Maier
, A. C.
Schwarze
, C. A.
Serván
, J.
Snyder
, and G.
St-Onge
, “Thresholding normally distributed data creates complex networks
,” Phys. Rev. E
101
, 062302
(2020
). 42.
T. L.
Frantz
, M.
Cataldo
, and K. M.
Carley
, “Robustness of centrality measures under uncertainty: Examining the role of network topology
,” Comput. Math. Organ. Theor.
15
, 303
–328
(2009
). 43.
M.
Bellingeri
, D.
Bevacqua
, F.
Scotognella
, R.
Alfieri
, Q.
Nguyen
, D.
Montepietra
, and D.
Cassi
, “Link and node removal in real social networks: A review
,” Front. Phys.
8
, 228
(2020
). 44.
V.
Latora
and M.
Marchiori
, “Vulnerability and protection of infrastructure networks
,” Phys. Rev. E
71
, 015103
(2005
). 45.
G.
Ghoshal
and A.-L.
Barabási
, “Ranking stability and super-stable nodes in complex networks
,” Nat. Commun.
2
, 394
(2011
). 46.
E.
Ceci
and S.
Barbarossa
, “Small perturbation analysis of network topologies,” in 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (IEEE, 2018), pp. 4194–4198.47.
M.
Tantardini
, F.
Ieva
, L.
Tajoli
, and C.
Piccardi
, “Comparing methods for comparing networks
,” Sci. Rep.
9
, 17557
(2019
). 48.
A.
Mheich
, F.
Wendling
, and M.
Hassan
, “Brain network similarity: Methods and applications
,” Network Neurosci.
4
, 507
–527
(2020
). 49.
T.
Rings
, T.
Bröhl
, and K.
Lehnertz
, “Network structure from a characterization of interactions in complex systems
,” Sci. Rep.
12
, 11742
(2022
). 50.
M. E. J.
Newman
, “Spread of epidemic disease on networks
,” Phys. Rev. E
66
, 016128
(2002
). 51.
S.
Bialonski
and K.
Lehnertz
, “Assortative mixing in functional brain networks during epileptic seizures
,” Chaos
23
, 033139
(2013
). 52.
M.
Barahona
and L. M.
Pecora
, “Synchronization in small-world systems
,” Phys. Rev. Lett.
89
, 054101
(2002
). 53.
F. M.
Atay
, T.
Bıyıkoğlu
, and J.
Jost
, “Network synchronization: Spectral versus statistical properties
,” Physica D
224
, 35
–41
(2006
). 54.
M. A.
Beauchamp
, “An improved index of centrality
,” Behav. Sci.
10
, 161
–163
(1965
). 55.
G.
Sabidussi
, “The centrality index of a graph
,” Psychometrika
31
, 581
–603
(1966
). 56.
L. C.
Freeman
, “A set of measures of centrality based on betweenness
,” Sociometry
40
, 35
–41
(1977
). 57.
L. C.
Freeman
, “Centrality in social networks: Conceptual clarification
,” Soc. Networks
1
, 215
–239
(1979
). 58.
P.
Bonacich
, “Power and centrality: A family of measures
,” Am. J. Sociol.
92
, 1170
–1182
(1987
). 59.
S.
Wuchty
and P. F.
Stadler
, “Centers of complex networks
,” J. Theor. Biol.
223
, 45
–53
(2003
). 60.
D.
Koschützki
, K.
Lehmann
, L.
Peeters
, S.
Richter
, D.
Tenfelde-Podehl
, and O.
Zlotowski
, “Centrality indices,” in Network Analysis, Lecture Notes in Computer Science Vol. 3418, edited by U. Brandes and T. Erlebach (Springer, Berlin, 2005), pp. 16–61.61.
S. P.
Borgatti
and M. G.
Everett
, “A graph-theoretic perspective on centrality
,” Soc. Networks
28
, 466
–484
(2006
). 62.
E.
Estrada
and D. J.
Higham
, “Network properties revealed through matrix functions
,” SIAM Rev.
52
, 696
–714
(2010
). 63.
T. W.
Valente
and K.
Fujimoto
, “Bridging: Locating critical connectors in a network
,” Soc. Netw.
32
, 212
–220
(2010
). 64.
D.
Chen
, L.
Lü
, M.-S.
Shang
, Y.-C.
Zhang
, and T.
Zhou
, “Identifying influential nodes in complex networks
,” Physica A
391
, 1777
–1787
(2012
). 65.
E. C.
Costa
, A. B.
Vieira
, K.
Wehmuth
, A.
Ziviani
, and A. P. C.
Da Silva
, “Time centrality in dynamic complex networks
,” Adv. Complex Syst.
18
, 1550023
(2015
). 66.
G.
Lawyer
, “Understanding the influence of all nodes in a network
,” Sci. Rep.
5
, 8665
(2015
). 67.
A.-K.
Wu
, L.
Tian
, and Y.-Y.
Liu
, “Bridges in complex networks
,” Phys. Rev. E
97
, 012307
(2018
). 68.
T.
Bröhl
and K.
Lehnertz
, “Centrality-based identification of important edges in complex networks
,” Chaos
29
, 033115
(2019
). 69.
N.
Zhao
, J.
Li
, J.
Wang
, T.
Li
, Y.
Yu
, and T.
Zhou
, “Identifying significant edges via neighborhood information
,” Physica A
548
, 123877
(2020
). 70.
T.
Bröhl
and K.
Lehnertz
, “A straightforward edge centrality concept derived from generalizing degree and strength
,” Sci. Rep.
12
, 4407
(2022
). 71.
L.
Lü
, D.
Chen
, X.-L.
Ren
, Q.-M.
Zhang
, Y.-C.
Zhang
, and T.
Zho
, “Vital nodes identification in complex networks
,” Phys. Rep.
650
, 1
–63
(2016
). 72.
G.
Iñiguez
, C.
Pineda
, C.
Gershenson
, and A.-L.
Barabási
, “Dynamics of ranking
,” Nat. Commun.
13
, 1646
(2022
). 73.
P.
Bonacich
, “Factoring and weighting approaches to status scores and clique identification
,” J. Math. Sociol.
2
, 113
–120
(1972
). 74.
A.
Bavelas
, “Communication patterns in task-oriented groups
,” J. Acoust. Soc. Am.
22
, 725
–730
(1950
). 75.
U.
Brandes
, “A faster algorithm for betweenness centrality
,” J. Math. Sociol.
25
, 163
–177
(2001
). 76.
M.
Girvan
and M. E. J.
Newman
, “Community structure in social and biological networks
,” Proc. Natl. Acad. Sci. U.S.A.
99
, 7821
–7826
(2002
). 77.
S.
Saavedra
, D. B.
Stouffer
, B.
Uzzi
, and J.
Bascompte
, “Strong contributors to network persistence are the most vulnerable to extinction
,” Nature
478
, 233
–235
(2011
). 78.
D. J.
Watts
and S. H.
Strogatz
, “Collective dynamics of ‘small-world’ networks
,” Nature
393
, 440
–442
(1998
). 79.
P.
Erdős
and A.
Rényi
, “On random graphs I
,” Publ. Math. Debrecen
6
, 290
–297
(1959
).80.
V.
Batagelj
and U.
Brandes
, “Efficient generation of large random networks
,” Phys. Rev. E
71
, 036113
(2005
). 81.
R.
Albert
and A.-L.
Barabási
, “Statistical mechanics of complex networks
,” Rev. Mod. Phys.
74
, 47
–97
(2002
). 82.
P.
Holme
, B. J.
Kim
, C. N.
Yoon
, and S. K.
Han
, “Attack vulnerability of complex networks
,” Phys. Rev. E
65
, 056109
(2002
). 83.
J.
Platig
, E.
Ott
, and M.
Girvan
, “Robustness of network measures to link errors
,” Phys. Rev. E
88
, 062812
(2013
). 84.
D. S.
Lekha
and K.
Balakrishnan
, “Central attacks in complex networks: A revisit with new fallback strategy
,” Physica A
549
, 124347
(2020
). 85.
C.
Martin
and P.
Niemeyer
, “Influence of measurement errors on networks: Estimating the robustness of centrality measures
,” Netw. Sci.
7
, 180
–195
(2019
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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