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Lu, Youjun; Guan, Yongqiu; Wei, Jiaying; Liang, Yanjun; Fu, Li; Zuo, Feiyu; Deng, Yunfeng

Joint degree distribution of growing multiplex network model with nonlinear preferential attachment rule. (English) Zbl 07773021

Cai, Zhiping (ed.) et al., Theoretical computer science. 40th national conference, NCTCS 2022, Changchun, China, July 29–31, 2022. Revised selected papers. Singapore: Springer. Commun. Comput. Inf. Sci. 1693, 26-42 (2022).
Summary: Many complex systems in real life are made up of several subsystems that evolve through time. Multiplex growth network models, in which edges reflect different types between the same vertex set, can be used to represent such systems. Here we put forward a new multiplex growth network model based on nonlinear preferential attachment rule. Firstly, we derive the general joint degree distribution expression of the model via the rate equation approach at the steady-state. Secondly, by using the Z-transform theory, we obtain the joint degree distribution of the model corresponding to the weight function \(f(k)=k\) and \(f(k)=c>0\). Finally, we apply Monte Carlo simulation to check the correctness of the theoretical analysis, the research shows that the theoretical results are corroborated with Monte Carlo simulations.
For the entire collection see [Zbl 1516.68008].

MSC:

05C82 Small world graphs, complex networks (graph-theoretic aspects)
65C05 Monte Carlo methods

Keywords:

multiplex network model; nonlinear preferential attachment rule; joint degree distribution

Software:

GenLouvain
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Full Text: DOI

References:

[1] Murphy, J.: Artificial intelligence, rationality, and the world wide web. IEEE Intell. Syst. 33(1), 98-103 (2018) · doi:10.1109/MIS.2018.012001557
[2] Pastor-Satorras, R., Vázquez, A., Vespignani, A.: Dynamical and correlation properties of the internet. Phys. Rev. Lett. 87(25), 258701 (2001) · Zbl 1087.68509
[3] Boltz, T.A., Devkota, P., Wuchty, S.: Collective influencers in protein interaction networks. Sci. Rep. 9, 3948 (2019) · doi:10.1038/s41598-019-40410-2
[4] Tabassum, S., Pereira, F.S.F., Fernandes, S., et al.: Social network analysis: an overview. WIREs Data Min. Knowl. Discov. 8, e1256 (2018)
[5] Lu, C., Zhang, Y., Ahn, Y.Y., Ding, Y., et al.: Co-contributorship network and division of labor in individual scientific collaborations. J. Assoc. Inf. Sci. Technol. 71(10), 1-17 (2020) · doi:10.1002/asi.24321
[6] Watts, D.J., Strogatz, S.H.: Collective dynamics of small world networks. Nature 393(6684), 440-442 (1998) · Zbl 1368.05139 · doi:10.1038/30918
[7] Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509-512 (1999) · Zbl 1226.05223 · doi:10.1126/science.286.5439.509
[8] Bianconi, G., Barabasi, A.L.: Bose-Einstein condensation in complex networks. Phys. Rev. Lett. 86(24), 5632-5635 (2001) · doi:10.1103/PhysRevLett.86.5632
[9] Li, X., Chen, G.R.: A local-world evolving network model. Phys. A 328(1-2), 274-286 (2003) · Zbl 1029.90502 · doi:10.1016/S0378-4371(03)00604-6
[10] Zadorozhnyi, V.N., Yudin, E.B.: Growing network: models following nonlinear preferential attachment rule. Phys. A 428, 111-132 (2015) · Zbl 1400.05216 · doi:10.1016/j.physa.2015.01.052
[11] Xiong, K., Zeng, C., Liu, Z.: Effect of degree correlation on the thermal transport in complex networks. Nonlinear Dyn. 94, 3067-3075 (2018). https://doi.org/10.1007/s11071-018-4545-y · doi:10.1007/s11071-018-4545-y
[12] Lewis, K., Kaufman, J., Gonzalez, M., et al.: Tastes, ties, and time: a new social network dataset using Facebook.com. Soc. Netw. 30(4), 330-342 (2008)
[13] Szell, M., Lambiotte, R., Thurner, R.: Multirelational organization of large-scale social networks in an online world. PNAS 107(31), 13636-13641 (2010) · doi:10.1073/pnas.1004008107
[14] Barigozzi, M., Fagiolo, G., Garlaschelli, D.: Multinetwork of international trade: a commodity-specific analysis. Phys. Rev. E 81(1), 046104 (2010) · doi:10.1103/PhysRevE.81.046104
[15] Halu, A., Mukherjee, S., Bianconi, G.: Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles. Phys. Rev. E 89(1), 012806 (2014) · doi:10.1103/PhysRevE.89.012806
[16] Kim, J.Y., Goh, K.I.: Coevolution and correlated multiplexity in multiplex networks. Phys. Rev. Lett. 111(5), 058702 (2013) · doi:10.1103/PhysRevLett.111.058702
[17] Nicosia, V., Bianconi, G., Latora, V., et al.: Growing multiplex networks. Phys. Rev. Lett. 111(5), 058701 (2013) · doi:10.1103/PhysRevLett.111.058701
[18] Nicosia, V., Bianconi, G., Latora, V., et al.: Nonlinear growth and condensation in multiplex networks. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 90(4), 042807 (2013)
[19] Fotouhi, B., Momeni, N.: Inter-layer degree correlations in heterogeneously growing multiplex networks. In: Mangioni, G., Simini, F., Uzzo, S.M., Wang, D. (eds.) Complex Networks VI. SCI, vol. 597, pp. 159-170. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-16112-9_16 · Zbl 1354.90024 · doi:10.1007/978-3-319-16112-9_16
[20] Momeni, N., Fotouhi, B.: Growing multiplex networks with arbitrary number of layers. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 92(6), 062812 (2015) · Zbl 1354.90024
[21] Lu, Y., Xu, D., Zhou, J.: Degree correlations in two layer growth model with nonlinear preferential attachment rule. In: Du, D., Li, L., Zhu, E., He, K. (eds.) NCTCS 2017. CCIS, vol. 768, pp. 167-181. Springer, Singapore (2017). https://doi.org/10.1007/978-981-10-6893-5_13 · doi:10.1007/978-981-10-6893-5_13
[22] Solá, L., Romance, M., Criado, R., et al.: Eigenvector centrality of nodes in multiplex networks. Chaos 23, 033131 (2013) · Zbl 1323.05117 · doi:10.1063/1.4818544
[23] Tudisco, F., Arrigo, F., Gautier, A.: Node and layer eigenvector centralities for multiplex networks. SIAM J. Appl. Math. 78(2), 853-876 (2018) · Zbl 06855293 · doi:10.1137/17M1137668
[24] Cangfeng, D., Kan, L.: Centrality ranking in multiplex networks using topologically biased random walks. Neurocomputing 312, 263-275 (2018) · doi:10.1016/j.neucom.2018.05.109
[25] Tortosa, L., Vicent, J.F., Yeghikyan, G.: An algorithm for ranking the nodes of multiplex networks with data based on the PageRank concept. Appl. Math. Comput. 392, 125676 (2021) · Zbl 1496.90018 · doi:10.1016/j.amc.2020.125676
[26] Baxter, G.J., Cellai, D., Dorogovtsev, S.N., et al.: Cycles and clustering in multiplex networks. Phys. Rev. E 94(6), 062308 (2016) · doi:10.1103/PhysRevE.94.062308
[27] Boccaletti, S., Bianconi, G., Criado, R., et al.: The structure and dynamics of multilayer networks. Phys. Rep. 544(1), 1-122 (2014) · doi:10.1016/j.physrep.2014.07.001
[28] Mucha, P.J., Richardson, T., Macon, K., et al.: Community structure in time-dependent, multiscale, and multiplex networks. Science 32(5980), 876-878 (2010) · Zbl 1226.91056 · doi:10.1126/science.1184819
[29] Newman, M.J., Girvan, M.: Finding and evaluating community structure in networks. Phys. Rev. E 69(2), 026113 (2004) · doi:10.1103/PhysRevE.69.026113
[30] Didier, G., Brun, C., Baudot, A.: Identifying communities from multiplex biological networks. PeerJ 3, e1525 (2015) · doi:10.7717/peerj.1525
[31] Ma, X., Dong, D., Wang, Q.: Community detection in multi-layer networks using joint nonnegative matrix factorization. IEEE Trans. Knowl. Data Eng. 31(2), 273-286 (2018) · doi:10.1109/TKDE.2018.2832205
[32] Gomez, S., Diaz-Guilera, A., Gomez-Gardenes, J., et al.: Diffusion dynamics on multiplex networks. Phys. Rev. Lett. 110(2), 028701 (2013) · doi:10.1103/PhysRevLett.110.028701
[33] Guo, Q., Lei, Y., Jiang, X., et al.: Epidemic spreading with activity-driven awareness diffusion on multiplex network. Chaos 26(4), 043110 (2016) · doi:10.1063/1.4947420
[34] Tejedor, A., Longjas, A., Foufoula-Georgiou, E., et al.: Diffusion dynamics and optimal coupling in multiplex networks with directed layers. Phys. Rev. X 8, 031071 (2018)
[35] Gao, S., Chang, L., Wang, X., et al.: Cross-diffusion on multiplex networks. New J. Phys. 22, 053047 (2020) · doi:10.1088/1367-2630/ab825e
[36] Jaquez, R.B., Ramos, L.A.A., Schaum, A.: Spreading control in two-layer multiplex networks. Entropy 22(10), 1157 (2020) · doi:10.3390/e22101157
[37] Yu, X., Yang, Q., Ai, K., et al.: Information spreading on two-layered multiplex networks with limited contact. IEEE Access 8, 104316-104325 (2020) · doi:10.1109/ACCESS.2020.2999495
[38] Gómez-Gardenes, J., Reiñares, I., Arenas, A., et al.: Evolution of cooperation in multiplex networks. Sci. Rep. 2, 620 (2012) · doi:10.1038/srep00620
[39] Pereda, M.: Evolution of cooperation under social pressure in multiplex networks. Phys. Rev. E 94(3), 032314 (2016) · doi:10.1103/PhysRevE.94.032314
[40] Yu, J., Liu, Z., Han, X.: Cooperation evolution in multiplex networks with the heterogeneous diffusion model. IEEE Access 9, 86074-86082 (2021) · doi:10.1109/ACCESS.2021.3084059
[41] Leyva, I., Sendiña-Nadal, I., Sevilla-Escoboza, R., Vera-Avila, V.P., et al.: Relay synchronization in multiplex networks. Sci. Rep. 8, 8629 (2017) · doi:10.1038/s41598-018-26945-w
[42] Jalan, S., Rathore, V., Kachhvah, A.D., et al.: Inhibition-induced explosive synchronization in multiplex networks. Phys. Rev. E 99(6), 062305 (2019) · doi:10.1103/PhysRevE.99.062305
[43] Guo, Q., Cozzo, E., Zheng, Z., et al.: Levy random walks on multiplex networks. Sci. Rep. 6, 37641 (2016) · doi:10.1038/srep37641
[44] Lu, Y.J., Xu, D.Y., Zhou, J.C.: Vertex degree distribution in growth models with nonlinear preferential attachment rule. J. Beijing Univ. Posts Telecommun. 39(5), 116-123 (2016)
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