Multilayer networks are the underlying structures of multiple real-world systems where we have more than one type of interaction/relation between nodes: social, biological, computer, or communication, to name only a few. In many cases, they are helpful in modeling processes that happen on top of them, which leads to gaining more knowledge about these phenomena. One example of such a process is the spread of influence. Here, the members of a social system spread the influence across the network by contacting each other, sharing opinions or ideas, or—explicitly—by persuasion. Due to the importance of this process, researchers investigate which members of a social network should be chosen as initiators of influence spread to maximize the effect. In this work, we follow this direction and develop and evaluate the sequential seeding technique for multilayer networks. Until now, such techniques were evaluated only using simple one layer networks. The results show that sequential seeding in multilayer networks outperforms the traditional approach by increasing the coverage and allowing to save the seeding budget. However, it also extends the duration of the spreading process.
REFERENCES
1.
D.
Kempe
, J.
Kleinberg
, and É.
Tardos
, “Maximizing the spread of influence through a social network,” in Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2003), pp. 137–146.2.
J.
Jankowski
, P.
Bródka
, P.
Kazienko
, B. K.
Szymanski
, R.
Michalski
, and T.
Kajdanowicz
, “Balancing speed and coverage by sequential seeding in complex networks
,” Sci. Rep.
7
, 891
(2017
). 3.
J.
Jankowski
, B. K.
Szymanski
, P.
Kazienko
, R.
Michalski
, and P.
Bródka
, “Probing limits of information spread with sequential seeding
,” Sci. Rep.
8
, 1
(2018
). 4.
M.
Kivelä
, A.
Arenas
, M.
Barthelemy
, J. P.
Gleeson
, Y.
Moreno
, and M. A.
Porter
, “Multilayer networks
,” J. Complex Netw.
2
, 203
–271
(2014
). 5.
R.
Michalski
, P.
Kazienko
, and J.
Jankowski
, “Convince a dozen more and succeed—The influence in multi-layered social networks,” in 2013 International Conference on Signal-Image Technology & Internet-Based Systems (IEEE, 2013), pp. 499–505.6.
S.
Boccaletti
, G.
Bianconi
, R.
Criado
, C. I.
Del Genio
, J.
Gómez-Gardenes
, M.
Romance
, I.
Sendina-Nadal
, Z.
Wang
, and M.
Zanin
, “The structure and dynamics of multilayer networks
,” Phys. Rep.
544
, 1
–122
(2014
). 7.
M.
De Domenico
, C.
Granell
, M. A.
Porter
, and A.
Arenas
, “The physics of spreading processes in multilayer networks
,” Nat. Phys.
12
, 901
–906
(2016
). 8.
P.
Bródka
, K.
Musial
, and J.
Jankowski
, “Interacting spreading processes in multilayer networks: A systematic review
,” IEEE Access
8
, 10316
–10341
(2020
). 9.
P.
Basaras
, G.
Iosifidis
, D.
Katsaros
, and L.
Tassiulas
, “Identifying influential spreaders in complex multilayer networks: A centrality perspective
,” IEEE Trans. Netw. Sci. Eng.
6
, 31
–45
(2017
). 10.
X.
Huang
, D.
Chen
, D.
Wang
, and T.
Ren
, “Identifying influencers in social networks
,” Entropy
22
, 450
(2020
). 11.
F.
Erlandsson
, P.
Bródka
, and A.
Borg
, “Seed selection for information cascade in multilayer networks,” in International Conference on Complex Networks and Their Applications (Springer, 2017), pp. 426–436.12.
M.
Magnani
and L.
Rossi
, “The ML-model for multi-layer social networks,” in 2011 International Conference on Advances in Social Networks Analysis and Mining (IEEE, 2011), pp. 5–12.13.
P.
Bródka
and P.
Kazienko
, “Multilayer social networks,” in Encyclopedia of Social Network Analysis and Mining, edited by R. Alhajj and J. Rokne (Springer New York, New York, 2018), pp. 1408–1422.14.
J.
Goldenberg
, B.
Libai
, and E.
Muller
, “Talk of the network: A complex systems look at the underlying process of word-of-mouth
,” Mark. Lett.
12
, 211
–223
(2001
). 15.
M.
Berlingerio
, M.
Coscia
, F.
Giannotti
, A.
Monreale
, and D.
Pedreschi
, “Foundations of multidimensional network analysis,” in 2011 International Conference on Advances in Social Networks Analysis and Mining (IEEE, 2011), pp. 485–489.16.
M.
Salehi
, R.
Sharma
, M.
Marzolla
, M.
Magnani
, P.
Siyari
, and D.
Montesi
, “Spreading processes in multilayer networks
,” IEEE Trans. Netw. Sci. Eng.
2
, 65
–83
(2015
). 17.
K.
Musiał
, P.
Kazienko
, and P.
Bródka
, “User position measures in social networks,” in Proceedings of the 3rd Workshop on Social Network Mining and Analysis: SNA-KDD ’09 (Association for Computing Machinery, New York, 2009).18.
Q.
Hu
, Y.
Gao
, P.
Ma
, Y.
Yin
, Y.
Zhang
, and C.
Xing
, “A new approach to identify influential spreaders in complex networks,” in International Conference on Web-Age Information Management (Springer, 2013), pp. 99–104.19.
L.
Page
, S.
Brin
, R.
Motwani
, and T.
Winograd
, “The PageRank citation ranking: Bringing order to the web,” Technical Report, Stanford InfoLab, 1999.20.
J.-X.
Zhang
, D.-B.
Chen
, Q.
Dong
, and Z.-D.
Zhao
, “Identifying a set of influential spreaders in complex networks
,” Sci. Rep.
6
, 27823
(2016
). 21.
L.
Seeman
and Y.
Singer
, “Adaptive seeding in social networks,” in 2013 IEEE 54th Annual Symposium on Foundations of Computer Science (IEEE, 2013), pp. 459–468.22.
A.
Sela
, I.
Ben-Gal
, A. S.
Pentland
, and E.
Shmueli
, “Improving information spread through a scheduled seeding approach,” in Proceedings of the 2015 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2015 (Association for Computing Machinery, 2015), pp. 629–632.23.
D.
Goldenberg
, A.
Sela
, and E.
Shmueli
, “Timing matters: Influence maximization in social networks through scheduled seeding
,” IEEE Trans. Comput. Social Syst.
5
, 621
–638
(2018
). 24.
A.
Sela
, D.
Goldenberg
, I.
Ben-Gal
, and E.
Shmueli
, “Active viral marketing: Incorporating continuous active seeding efforts into the diffusion model
,” Expert Syst. Appl.
107
, 45
–60
(2018
). 25.
J.-L.
He
, Y.
Fu
, and D.-B.
Chen
, “A novel top-k strategy for influence maximization in complex networks with community structure
,” PloS One
10
, e0145283
(2015
). 26.
C.
Ni
, J.
Yang
, and D.
Kong
, “Sequential seeding strategy for social influence diffusion with improved entropy-based centrality
,” Physica A
545
, 123659
(2020
).27.
Q.
Liu
and T.
Hong
, “Sequential seeding for spreading in complex networks: Influence of the network topology
,” Physica A
508
, 10
–17
(2018
). 28.
J.
Jankowski
, P.
Bródka
, R.
Michalski
, and P.
Kazienko
, “Seeds buffering for information spreading processes,” in International Conference on Social Informatics (Springer, 2017), pp. 628–641.29.
J.
Jankowski
, M.
Waniek
, A.
Alshamsi
, P.
Bródka
, and R.
Michalski
, “Strategic distribution of seeds to support diffusion in complex networks
,” PloS One
13
, e0205130
(2018
). 30.
R.
Michalski
, J.
Jankowski
, and P.
Bródka
, “Effective influence spreading in temporal networks with sequential seeding
,” IEEE Access
8
, 151208
–151218
(2020
). 31.
L.
Rossi
and M.
Magnani
, “Towards effective visual analytics on multiplex and multilayer networks
,” Chaos, Solitons Fractals
72
, 68
–76
(2015
). 32.
J.
Coleman
, E.
Katz
, and H.
Menzel
, “The diffusion of an innovation among physicians
,” Sociometry
20
, 253
–270
(1957
). 33.
A.
Cardillo
, J.
Gómez-Gardenes
, M.
Zanin
, M.
Romance
, D.
Papo
, F.
Del Pozo
, and S.
Boccaletti
, “Emergence of network features from multiplexity
,” Sci. Rep.
3
, 1344
(2013
). 34.
T. A.
Snijders
, P. E.
Pattison
, G. L.
Robins
, and M. S.
Handcock
, “New specifications for exponential random graph models
,” Sociol. Methodol.
36
, 99
–153
(2006
). 35.
M.
Magnani
and L.
Rossi
, “Formation of multiple networks,” in International Conference on Social Computing, Behavioral-Cultural Modeling, and Prediction (Springer, 2013), pp. 257–264.36.
M.
Matteo
, V.
Davide
, and D.
Mikael
, Multinet: Analysis and Mining of Multilayer Social Networks
(CRAN
, 2020
), available at https://cran.r-project.org/web/packages/multinet/index.html.37.
B. A.
Hassan
and T. A.
Rashid
, “Operational framework for recent advances in backtracking search optimisation algorithm: A systematic review and performance evaluation
,” Appl. Math. Comput.
370
, 124919
(2020
). 38.
M.
De Domenico
, A.
Lancichinetti
, A.
Arenas
, and M.
Rosvall
, “Identifying modular flows on multilayer networks reveals highly overlapping organization in interconnected systems
,” Phys. Rev. X
5
, 011027
(2015
). 39.
S.
Iyer
and L. A.
Adamic
, “The costs of overambitious seeding of social products,” in International Conference on Complex Networks and Their Applications (Springer, 2018), pp. 273–286.40.
F. M.
Bass
, “A new product growth for model consumer durables
,” Manage. Sci.
15
, 215
–227
(1969
). 41.
W.
Rand
and R. T.
Rust
, “Agent-based modeling in marketing: Guidelines for rigor
,” Int. J. Res. Mark.
28
, 181
–193
(2011
). 42.
M.
Chica
and W.
Rand
, “Building agent-based decision support systems for word-of-mouth programs: A freemium application
,” J. Mark. Res.
54
, 752
–767
(2017
). 43.
M.
Scatà
, A.
Di Stefano
, P.
Liò
, and A.
La Corte
, “The impact of heterogeneity and awareness in modeling epidemic spreading on multiplex networks
,” Sci. Rep.
6
, 1
(2016
). 44.
H.
Zang
, “The effects of global awareness on the spreading of epidemics in multiplex networks
,” Physica A
492
, 1495
–1506
(2018
). 45.
R. A.
Holley
and T. M.
Liggett
, “Ergodic theorems for weakly interacting infinite systems and the voter model
,” Ann. Probab.
3
, 643
–663
(1975
). 46.
P.
Bródka
, J.
Jankowski
, and R.
Michalski
, see for “Sequential Seeding in Multilayer Networks” (2021).47.
P.
Bródka
, J.
Jankowski
, and R.
Michalski
, “Replication code and data for Sequential Seeding in Multilayer Networks
,” Zenodo (2021
). © 2021 Author(s).
2021
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