多重网络中的非线性增长与凝聚
Non-linear growth and condensation in multiplex networks
摘要：
不同类型的相互作用共存并共同进化，以塑造多元化网络的结构和功能。在这里，我们提出了一个一般类的增长模型中，通过一组非线性的优先连接规则的多路网络的各个层共同发展。我们表明，无论是数值和分析，通过调整非线性的水平，这些模型允许再现均匀或异质的程度分布，以及积极或消极的程度相关层。特别是，我们推导出了出现凝聚态的条件，其中每层中的一个节点吸引了所有边缘的大部分。
英文摘要：
Different types of interactions coexist and coevolve to shape the structure and function of a multiplex network. We propose here a general class of growth models in which the various layers of a multiplex network coevolve through a set of non-linear preferential attachment rules. We show, both numerically and analytically, that by tuning the level of non-linearity these models allow to reproduce either homogeneous or heterogeneous degree distributions, together with positive or negative degree correlations across layers. In particular, we derive the condition for the appearance of a condensed state in which one node in each layer attracts an extensive fraction of all the edges.
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