面向在线社会网络的爆炸渗流模型的研究

Percolation in random networks is a phase transition from small scattered clusters to large-scale connectivity. The phase transition of the classical Erdos-Renyi (ER) random percolation is robust first order, or continuous at the phase transition critical point. It is an outstanding challenge to understand the underlying mechanism for second order transition, or discontinuous transition in the field of statistical physics. In recent years, some models which are based on ER random graph, are proposed in which the order parameter and scaling behavior show some characteristics of discontinuous transition, which are thus called "explosive percolation". However, the percolation in real networked systems is usually restricted by the underlying network. An important example is online social networks, such as microblog, facebook, BBS and so on. In online social networks, the social relationships between individuals are diverse and highly influential to each other, which make a heterogeneous, directed, weighted and large-scale networked system. In this proposal, we study the critical behaviors of various explosive percolation models in scale-free networks,directed networks and weighted networks, such as discontinuity of phase transition, scaling behavior and other properties like multiple giant components. This proposal aims at not only developing the theory of explosive percolation, but also help understanding the mechanism of information diffusion in online social networks.

随机图上的渗流模型是刻画网络结构从大量离散的小连通分量到形成巨大连通分量的相变过程。经典的Erdos-Renyi随机渗流模型在临界相变点产生了二级相变，即连续相变。一级相变（不连续相变）的产生机理成为统计物理领域的重要难题。近几年来统计物理学家基于Erdos-Renyi随机渗流模型提出了爆炸渗流模型，其序参量和标度行为都具有不连续相变的特征。然而真实系统的渗流往往受到基础网络结构的限制，例如微博、facebook、网络论坛等在线社会网络上的信息传播。在线社会网络由于个体之间多种类型且相互影响的社会关系逐步发展成为无尺度度分布、有向、带权的大规模复杂网络系统。本项目将基于在线社会网络的拓扑结构特征，研究无尺度网络、有向网络、带权网络下的各种爆炸渗流模型相变的不连续性、标度行为等临界现象。该研究不仅是对爆炸渗流理论的重要发展和补充，对于在线社会网络信息传播问题的研究也有重要的指导意义。

本项目旨在基于在线社会网络的拓扑结构特征，研究无尺度网络、有向网络、带权.网络下的各种爆炸渗流模型相变的不连续性、标度行为等临界现象。我们主要开展.了五个方面的研究：（1）研究了无尺度网络结构下的BFW爆炸渗流模型的渗流相变.不连续性和相变临界性质（2）研究了金融交易股票价格网络的同步行为和奇美拉.现象。（3）针对BFW爆炸渗流模型的不连续相变发生的早期特征和离散尺度不变性.展开研究（4）针对BFW爆炸渗流模型的多次相变现象展开研究（5）对BFW爆炸性渗.流模型的研究进展进行了综述并提出了后续研究课题。研究成果发表5篇SCI论文，.1部专著。