Public opinion quickly generated and propagated on online social networks brings huge influences on society and state security. Previous studies mostly analyze its snapshot in a short-term time interval to predict and control the explosive size, but neglect its long-term evolutionary process. In this paper, based on the online social network of Sina Weibo, we trace nine public opinion events in the nearly two-year duration to comprehensively observe the long-term evolutionary processes and characterize the temporal dynamics and propagating networks. The long-term evolutionary processes of public opinion are constructed by quantitatively measuring forwarding sizes at a daily scale. We show their non-Markov temporal dynamics by autocorrelation analysis, which is verified by the heavy-tail interval time distribution of individual forwarding behaviors. Also, the temporally propagating networks are abstracted from individual forwarding behaviors to represent the microcosmic organization of forming public opinion. The topological analysis of aggregating propagating networks shows that the microcosmic organization is generally constructed by a giant connected component and amounts of small connected components with strongly heterogeneous cascade sizes, and the corresponding degree distributions obeys a power law which is shaped by the giant connected component. Furthermore, we compare the follower–followee (i.e. friendship) network with the propagating network to unveil their potential correlation, and find that at large scale they behave a similar connection pattern. This work first projects public opinion into a process-based model to study its temporal dynamics and helps us to better understand the underlying mechanics of forming public opinion.

中文翻译：

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舆论长期演化过程的时间传播网络方法

舆论在网络社交网络上迅速产生和传播，给社会和国家安全带来巨大影响。以往的研究大多分析其短期时间间隔内的快照以预测和控制爆炸大小，而忽略了其长期演化过程。本文基于新浪微博在线社交网络，追踪近两年时间里的九个舆情事件，全面观察长期演化过程，刻画时间动态和传播网络。舆论的长期演化过程是通过在每日尺度上定量测量转发规模来构建的。我们通过自相关分析展示了它们的非马尔可夫时间动态，并通过个体转发行为的重尾间隔时间分布验证了这一点。此外，时间传播网络是从个人转发行为中抽象出来的，代表形成舆论的微观组织。聚合传播网络的拓扑分析表明，微观组织一般由一个巨大的连通分量和大量级联大小异质性很强的小连通分量构成，其对应的度分布服从由巨型连通分量形成的幂律。此外，我们将追随者-追随者（即友谊）网络与传播网络进行比较，以揭示它们的潜在相关性，并发现它们在大范围内表现出相似的连接模式。