Sun Jun, Medo Matúš, Staab Steffen
Institute for Web Science and Technologies, Universität Koblenz-Landau, 56070 Koblenz, Germany.
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, People's Republic of China; Department of Radiation Oncology, Inselspital, Bern University Hospital and University of Bern, 3010 Bern, Switzerland; and Department of Physics, University of Fribourg, 1700 Fribourg, Switzerland.
Phys Rev E. 2020 Feb;101(2-1):022309. doi: 10.1103/PhysRevE.101.022309.
Preferential attachment drives the evolution of many complex networks. Its analytical studies mostly consider the simplest case of a network that grows uniformly in time despite the accelerating growth of many real networks. Motivated by the observation that the average degree growth of nodes is time invariant in empirical network data, we study the degree dynamics in the relevant class of network models where preferential attachment is combined with heterogeneous node fitness and aging. We propose an analytical framework based on the time invariance of the studied systems and show that it is self-consistent only for two special network growth forms: the uniform and the exponential network growth. Conversely, the breaking of such time invariance explains the winner-takes-all effect in some model settings, revealing the connection between the Bose-Einstein condensation in the Bianconi-Barabási model and similar gelation in superlinear preferential attachment. Aging is necessary to reproduce realistic node degree growth curves and can prevent the winner-takes-all effect under weak conditions. Our results are verified by extensive numerical simulations.
偏好依附驱动着许多复杂网络的演化。其分析研究大多考虑网络最简单的情况，即网络随时间均匀增长，尽管许多真实网络的增长在加速。受经验网络数据中节点平均度增长是时间不变性这一观察结果的启发，我们研究了相关类别的网络模型中的度动态，其中偏好依附与节点的异质适应性和老化相结合。我们基于所研究系统的时间不变性提出了一个分析框架，并表明它仅对于两种特殊的网络增长形式是自洽的：均匀网络增长和指数网络增长。相反，这种时间不变性的打破解释了某些模型设置中的赢者通吃效应，揭示了比安科尼 - 巴拉巴西模型中的玻色 - 爱因斯坦凝聚与超线性偏好依附中类似凝胶化之间的联系。老化对于重现现实的节点度增长曲线是必要的，并且在弱条件下可以防止赢者通吃效应。我们的结果通过广泛的数值模拟得到了验证。
