论文标题
在弱耦合网络中的扩散和共识
Diffusion and Consensus in a Weakly Coupled Network of Networks
论文作者
论文摘要
我们研究网络模型网络中的扩散和共识动态。在此模型中，有一个子网络集合，使用少量链接相互连接。我们考虑一个设置网络之间的链接具有较小的权重，或者使用的频率少于每个子网络中的链接。使用光谱扰动理论，我们分析了研究系统的扩散率和收敛速率。我们的分析表明，扩散率和收敛速率的一阶近似与单个图的拓扑无关。速率仅取决于每个图中的节点数量和连接边缘的拓扑数。第二阶分析显示了每个子网络中连接节点的扩散和收敛速率之间的关系。我们通过数值示例进一步强调了这些理论结果。
We study diffusion and consensus dynamics in a Network of Networks model. In this model, there is a collection of sub-networks, connected to one another using a small number of links. We consider a setting where the links between networks have small weights, or are used less frequently than links within each sub-network. Using spectral perturbation theory, we analyze the diffusion rate and convergence rate of the investigated systems. Our analysis shows that the first order approximation of the diffusion and convergence rates is independent of the topologies of the individual graphs; the rates depend only on the number of nodes in each graph and the topology of the connecting edges. The second order analysis shows a relationship between the diffusion and convergence rates and the information centrality of the connecting nodes within each sub-network. We further highlight these theoretical results through numerical examples.
