论文标题
优先依恋网络模型中的时间不变程度增长
Time-invariant degree growth in preferential attachment network models
论文作者
论文摘要
优先附件驱动许多复杂网络的演变。它的分析研究大多考虑了尽管许多真实网络的增长加速增长，该网络中最简单的案例会逐渐增长。通过观察到节点的平均程度增长在经验网络数据中是时间不变的，我们研究了相关网络模型类别的程度动力学，其中优先附着与异质节点的适应性和衰老相结合。我们提出了一个基于研究系统的时间变化的新分析框架，并表明它仅对两种特殊网络增长形式是自一致的：统一和指数的网络增长。相反，这种时间不变的破坏解释了在某些模型设置中的获胜者效果，从而揭示了Bianconi-Barabási模型中Bose-Einstein凝结与超线性优先附件中类似的凝胶化之间的联系。衰老是重现逼真的节点度增长曲线所必需的，并且可以防止在弱条件下赢得胜利的效果。我们的结果通过广泛的数值模拟得到验证。
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 a novel 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 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.
