Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA.
Phys Rev Lett. 2009 Nov 6;103(19):198701. doi: 10.1103/PhysRevLett.103.198701. Epub 2009 Nov 4.
We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion of social "balance" allows us to define an energy landscape for such networks. Its structure is complex: numerical experiments reveal a landscape dimpled with local minima of widely varying energy levels. We derive rigorous bounds on the energies of these local minima and prove that they have a modular structure that can be used to classify them.
我们将紧密联系的朋友和敌人社区建模为一个完全连接的网络，其边缘带有正号和负号。社会心理学理论表明，某些符号模式比其他模式更稳定。这种社会“平衡”的概念使我们能够为这样的网络定义一个能量景观。它的结构很复杂：数值实验揭示了一个带有局部极小值的能量景观，这些局部极小值的能量水平差异很大。我们推导出了这些局部极小值的能量的严格界限，并证明它们具有模块化结构，可以用来对它们进行分类。
