Antal T, Krapivsky P L, Redner S
Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Sep;72(3 Pt 2):036121. doi: 10.1103/PhysRevE.72.036121. Epub 2005 Sep 21.
We study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes. The network is endowed with dynamics in which the sense of a link in an imbalanced triad--a triangular loop with one or three unfriendly links--is reversed to make the triad balanced. With this dynamics, an infinite network undergoes a dynamic phase transition from a steady state to "paradise"--all links are friendly--as the propensity p for friendly links in an update event passes through 1/2 . A finite network always falls into a socially balanced absorbing state where no imbalanced triads remain. If the additional constraint that the number of imbalanced triads in the network not increase in an update is imposed, then the network quickly reaches a balanced final state.
我们研究包含个体节点之间友好和不友好双边链接的社交网络的演化。该网络具有这样一种动态特性：不平衡三元组（即带有一条或三条不友好链接的三角形回路）中的链接方向会反转，以使三元组达到平衡。在这种动态特性下，当更新事件中友好链接的倾向p超过1/2时，无限网络会经历从稳态到“天堂”（所有链接都是友好的）的动态相变。有限网络总是会陷入一种社会平衡的吸收态，即不存在不平衡三元组。如果施加网络中不平衡三元组数量在更新时不增加的附加约束，那么网络会迅速达到平衡的最终状态。
