[目的/意义]提出和构建网络舆情衍进指数，以描述网络舆情演化过程中常衍生出新的子话题的现象，对于舆情预警、预测具有重要的理论及实践意义。[方法/过程]以文本聚类结果和文本聚类有效性为依据，提出网络舆情衍进的判别标准和舆情衍进指数的构建过程，并以"教科书老赖"这一事件作为样本数据进行实证分析。[结果/结论]所构建的舆情衍进速率指数可以用于描述舆情衍进。在突发期阶段话题舆情衍进指数最高，此后逐渐下降，这一阶段的舆情衍进最为剧烈，子话题的出现呈现爆发性增长；舆情衍进指数在舆情蔓延期内出现阶梯式下降，此后保持为负值，舆情的子话题开始逐渐减少，舆情内容本身由发散转为收敛；进入消散期后，子话题数量趋于稳定。作为舆情衍进速率的测度和舆情衍进的判别方式，舆情衍进指数为舆情监管和舆情预警提供了全新的角度。

[Purpose/significance] During the evolution of public opinion, the derivation of public opinion could possess significant value for the forecasting and warning of public opinion both theoretically and empirically.[Method/process] To investigate the mechanism of public opinion derivation, this paper conducted the study using text clustering and DB cluster validity index. It proposed certain standards to judge the occurrence of public opinion derivation and its according velocity index. Furthermore, this paper used an well-known public opinion incident called "Classic Deadbeat" to conduct an empirical research.[Result/conclusion] The result of empirical study shows that:the derivative index reaches its climax during emergence phase and declined thereafter. The number of sub-topics reaches its climax during the integration phase and then declined thereafter; when the number of sub-topics decreased, the derivative index become negative,indicating that the public opinion become stabilized. When the public opinion incident reaches the disappearance phase, the number of sub topics become stable and the derivative index remain negative but approach zero. The study of derivative index of public opinion offers a new angle to study public opinion observation and prediction.