Abstract
Nodes distribution by degrees is the most important characteristic of complex networks. For SF-networks it follows a power law. While degree distribution is a first order graph metric, the assortativity is a second order one. The concept of assortativity is extensively using in network analysis. In general degree distribution forms an essential restriction both on the network structure and on assortativity coefficient boundaries. The problem of determining the structure of BA-networks having an extreme assortativity coefficient is considered. Greedy algorithms for generating BA-networks with extreme assortativity have been proposed. As it was found, an extremely disassortative BA-network is asymptotically bipartite, while an extremely assortative one is close to be a set of complete and disconnected clusters. The estimates of boundaries for assortativity coefficient have been found. These boundaries are narrowing with increasing the network size and are significantly narrower than for networks having an arbitrary structure.
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References
Newman M (2003) Mixing patterns in networks. Phys Rev E 67
Dorogovtsev N, Mendes J (2002) Evolution of networks. Adv Phys 51(4):1079–1187
Shergin VL, Chala LE, Udovenko SG (2018) Fractal dimension of infinitely growing discrete sets. In: 2018 14th international conference on advanced trends in radioelectronics, telecommunications and computer engineering (TCSET), Slavske, pp 259–263. https://doi.org/10.1109/TCSET.2018.8336198
Kirichenko L, Radivilova T, Bulakh V (2018) Classification of fractal time series using recurrence plots. In: 2018 international scientific-practical conference problems of infocommunications. Science and technology (PIC S&T). IEEE, pp 719–724. https://doi.org/10.1109/infocommst.2018.8632010
Noldus R, Van Mieghem P (2015) Assortativity in complex networks. J Complex Netw 3:507–542
Shergin V, Chala L (2017) The concept of elasticity of scale-free networks. In: 2017 4th international scientific-practical conference problems of infocommunications. Science and technology (PIC S&T), Kharkov, pp 257–260. https://doi.org/10.1109/INFOCOMMST.2017.8246392
Peel L, Delvenne JC, Lambiotte R (2017) Multiscale mixing patterns in networks. Proc Natl Acad Sci 115. https://doi.org/10.1073/pnas.1713019115
Muscoloni A, Cannistraci CV (2017) Rich-clubness test: how to determine whether a complex network has or doesn’t have a rich-club? In: The 6th international conference on complex networks & their applications, Lyon (France), 29 Nov–01 Dec 2017, pp 291–293
Ageyev DV, Ignatenko AA, Wehbe F (2013) Design of information and telecommunication systems with the usage of the multi-layer graph model. In: Proceedings of the XIIth international conference on the experience of designing and application of CAD systems in microelectronics (CADSM). Lviv Polytechnic National University, Lviv-Polyana, Ukraine, pp 1–4
Ageyev D et al (2018) Classification of existing virtualization methods used in telecommunication networks. In: Proceedings of the 2018 IEEE 9th international conference on dependable systems, services and technologies (DESSERT), pp 83–86
Kryvinska N (2010) Converged network service architecture: a platform for integrated services delivery and interworking. In: Electronic business series, vol 2. International Academic Publishers, Peter Lang Publishing Group
Kirichenko L, Radivilova T, Zinkevich I (2018) Comparative analysis of conversion series forecasting in E-commerce tasks. In: Shakhovska N, Stepashko V (eds) Advances in intelligent systems and computing II. CSIT 2017. Advances in intelligent systems and computing, vol 689. Springer, Cham, pp 230–242. https://doi.org/10.1007/978-3-319-70581-1_16
Shergin V, Chala L, Udovenko S (2019) Assortativity properties of scale-free networks. In: 2019 international scientific-practical conference problems of infocommunications. Science and technology (PIC S&T). IEEE, pp 92–96
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Shergin, V., Udovenko, S., Chala, L. (2021). Assortativity Properties of Barabási-Albert Networks. In: Radivilova, T., Ageyev, D., Kryvinska, N. (eds) Data-Centric Business and Applications. Lecture Notes on Data Engineering and Communications Technologies, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-030-43070-2_4
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