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A node model is proposed to study the self-organized criticality in the small-world networks which represent the social networks.Based on the node model and the social balance dynamics,the social networks are mapped to the thermodynamic systems and the phenomena are studied with physical methods.It is found that the avalanche in the small-world networks at the critical state satisfies the power-law distribution spatially and temporally.The balance dynamics on social networks[1] based on the notion of social balance has been studied.[2-4]In Ref.[2],the authors studied the triad balance dynamic on a completely connected network representing a social network.At each step,they choose a triad relation from the social network and let it evolve.When the network gets dynamically balanced,they will reach the distributions of each triad relation.Moreover,other researchers subsequently carried out several studies on balance dynamics.[5,6]In this Letter,a node model is proposed to describe the triad relations,so the edge relations in Ref.[2] are changed to node relations,which may be more a universal method to study the phenomena in social networks.We will introduce the node model later.