Modeling Clustered Scale-free Networks by Applying Various Preferential Attachment Patterns

Abstract

Preferential attachment phenomenon is a key factor providing scale-free behavior in complex networks. In this study, we introduced various preferential attachment patterns applied in a growing Barabasi-Albert network, denoted by a factor α. We first generated networks under constant preferential attachment levels from 0 to 2, where 1 stands for linear preferential attachment. Then we performed network simulations under uniformly distributed random α condition, within the interval [0,2]. Although mean α is 1 for this setup, generated networks displayed greater clustering together with lower modularity and separation values compared to the setup with α=1. We also performed similar network generation procedures with various distribution functions applied for α, each resulting random levels of preferential attachment. We achieved networks with power-law consistent degree distributions with γ coefficients between 2 and 3, together with improved clustering coefficients up to ~0.3. As a result, scale-free network topologies featuring greater clustering levels compared to pure Barabasi-Albert model are achieved. 

Keywords

• Complex network modeling,Preferential attachment,Scale-free networks,Clustering coefficient

References

1. Abbasi, A., Hossain, L., & Leydesdorff, L. (2012). Betweenness centrality as a driver of preferential attachment in the evolution of research collaboration networks. Journal of Informetrics, 6(3), 403-412. Albert, R., & Barabási, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47-97. doi: 10.1103/RevModPhys.74.47 Alstott, J., Klymko, C., Pyzza, P. B., & Radcliffe, M. (2016). Local rewiring algorithms to increase clustering and grow a small world. arXiv preprint arXiv:1608.02883. Bansal, S., Khandelwal, S., & Meyers, L. A. (2009). Exploring biological network structure with clustered random networks. BMC bioinformatics, 10(1), 405. Barabási, A. L. (2016). Network Science. Cambridge: Cambridge University Press. Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509-512. doi: 10.1126/science.286.5439.509 Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-Law Distributions in Empirical Data. Siam Review, 51(4), 661-703. doi: 10.1137/070710111 Colomer-de-Simon, P., & Boguná, M. (2012). Clustering of random scale-free networks. Physical Review E, 86(2), 026120. Dereich, S., & Mörters, P. (2009). Random networks with sublinear preferential attachment: degree evolutions. Electronic Journal of Probability, 14, 1222-1267. Dereich, S., & Mörters, P. (2011). Random networks with concave preferential attachment rule. Jahresbericht der Deutschen Mathematiker-Vereinigung, 113(1), 21-40. Herrero, C. P. (2015). Ising model in clustered scale-free networks. Physical Review E, 91(5), 052812. Holme, P., & Kim, B. J. (2002). Growing scale-free networks with tunable clustering. Physical Review E, 65(2). doi: 10.1103/PhysRevE.65.026107 Jeong, H., Néda, Z., & Barabási, A.-L. (2003). Measuring preferential attachment in evolving networks. EPL (Europhysics Letters), 61(4), 567. Johnson, S. L., Faraj, S., & Kudaravalli, S. (2014). Emergence of Power Laws in Online Communities: The Role of Social Mechanisms and Preferential Attachment. Mis Quarterly, 38(3), 795-808. Kim, J., & Diesner, J. (2017). Over-time measurement of triadic closure in coauthorship networks. Social Network Analysis and Mining, 7(1), 9. doi: 10.1007/s13278-017-0428-3 Manna, S. S., & Sen, P. (2002). Modulated scale-free network in Euclidean space. Physical Review E, 66(6), 066114. Milojević, S. (2010). Modes of collaboration in modern science: Beyond power laws and preferential attachment. Journal of the Association for Information Science and Technology, 61(7), 1410-1423. Newman, M. E. J. (2003). The structure and function of complex networks. Siam Review, 45(2), 167-256. doi: 10.1137/s003614450342480 Poncela, J., Gómez-Gardenes, J., Floría, L. M., Sánchez, A., & Moreno, Y. (2008). Complex cooperative networks from evolutionary preferential attachment. Plos One, 3(6), e2449. Türker, İ. (2018). Generating clustered scale-free networks using Poisson based localization of edges. Physica A: Statistical Mechanics and its Applications, 497, 72-85. doi: https://doi.org/10.1016/j.physa.2018.01.009 Xie, Z., Ouyang, Z., & Li, J. (2016). A geometric graph model for coauthorship networks. Journal of Informetrics, 10(1), 299-311. Xulvi-Brunet, R., & Sokolov, I. M. (2002). Evolving networks with disadvantaged long-range connections. Physical Review E, 66(2), 026118.