Abstract: In our everyday social life, there exist many scenarios that users are affected by each other, and decisions are made collaboratively. This paper deeply investigates the behavior diffusion model and diffusion process in social network, based on mean-field theory. A specific diffusion model is desiged that can accommodate the impact of three factors on user’s probability of adopting one specific behavior：the absolute number and the ratio of neighbors adopting the behavior and the number of her total neighbors. Based on mean-field theory, the diffusion process is analytically provided, and the effect of network structure on behavior diffusion is also given. The necessary condition（critical threshold） for widespread diffusion is analyzed. The simulation results verify the theoretical analysis.

Key words: social network, mean-field theory, behavior diffusion, critical threshold

摘要： 在社会生活中，存在大量的用户之间相互影响相互协调并做出决策的事例，具有广泛的应用。深入研究了基于平均场理论的复杂社会网络中行为扩散模式。设计了特定的扩散模型，该模型考虑了采用某行为的邻居节点绝对数目、相对比率以及节点的总邻居数目对该节点选择行为的影响。采用平均场理论对扩散过程进行分析，研究了网络结构对行为扩散的影响，从理论上得出了如何选择门限值使新行为能够在社会网络中大规模传播成为可能。

关键词: 社会网络, 平均场理论, 行为扩散, 门限值