Department of Systems Science, School of Management, Beijing Normal University, Beijing 100875, People's Republic of China.
Chaos. 2013 Mar;23(1):013104. doi: 10.1063/1.4773823.
Many real-world networks display a natural bipartite structure, yet analyzing and visualizing large bipartite networks is one of the open challenges in complex network research. A practical approach to this problem would be to reduce the complexity of the bipartite system while at the same time preserve its functionality. However, we find that existing coarse graining methods for monopartite networks usually fail for bipartite networks. In this paper, we use spectral analysis to design a coarse graining scheme specific for bipartite networks, which keeps their random walk properties unchanged. Numerical analysis on both artificial and real-world networks indicates that our coarse graining can better preserve most of the relevant spectral properties of the network. We validate our coarse graining method by directly comparing the mean first passage time of the walker in the original network and the reduced one.
许多真实世界的网络呈现出自然的二分结构，然而分析和可视化大型二分网络是复杂网络研究中的一个开放性挑战。解决这个问题的一种实用方法是在保持其功能的同时降低二分系统的复杂性。然而，我们发现现有的用于单分网络的粗粒化方法通常不适用于二分网络。在本文中，我们使用谱分析设计了一种特定于二分网络的粗粒化方案，该方案保持了它们的随机游走性质不变。对人工和真实网络的数值分析表明，我们的粗粒化可以更好地保留网络的大部分相关谱性质。我们通过直接比较原始网络和简化网络中漫游者的平均首次通过时间来验证我们的粗粒化方法。
