非平衡增长网络的熵率
Entropy rate of non-equilibrium growing networks
摘要：
最近引入了新的熵测度来量化网络的复杂性。这些熵测度大多适用于静态网络或定义在静态复杂网络上的动态过程。本文定义了增长网络模型的熵率。这个熵率量化了增长的网络模型通常会生成多少个标记网络。我们分析评估增长树网络模型的熵率和具有相同渐近度分布的树网络的熵之间的差异。我们发现，动态模型产生的线性偏好连接的增长网络是指数小于静态网络具有相同的度分布的各种相关的增长网络模型。我们研究了具有结构相变的增长网络模型的熵率，包括具有非线性优先连接的模型。最后，我们带来的数值证据表明，熵率以上和以下的结构相变遵循不同的缩放与网络的大小。
英文摘要：
New entropy measures have been recently introduced for the quantification of the complexity of networks. Most of these entropy measures apply to static networks or to dynamical processes defined on static complex networks. In this paper we define the entropy rate of growing network models. This entropy rate quantifies how many labeled networks are typically generated by the growing network models. We analytically evaluate the difference between the entropy rate of growing tree network models and the entropy of tree networks that have the same asymptotic degree distribution. We find that the growing networks with linear preferential attachment generated by dynamical models are exponentially less than the static networks with the same degree distribution for a large variety of relevant growing network models. We study the entropy rate for growing network models showing structural phase transitions including models with non-linear preferential attachment. Finally, we bring numerical evidence that the entropy rate above and below the structural phase transitions follow a different scaling with the network size.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
