The development of complexity science has not only triggered changes in the natural sciences but has also increasingly penetrated into the fields of philosophy and humanities and social sciences. Enlightened by many ideas on traditional statistical physics, we find that the time correlation functions can be used as a powerful tool to detect the collective behavior in temporal systems. Disregard of specific models, the correlation functions are widely applicable to a variety of different systems. With 4 different networks collected from open access, we devise a delayed time correlation functions which measures the statistical correlation of a specific user and the response of the public. We also study the properties of the correlation function in the data sets in detail in order to find the possible logistic causality of the collective phenomena of the users. The results suggest that the correlation function provides the underlying dynamic property of the information spreading on the network. The correlation function summarizes all the possible factors (known or unknown yet) that could make a contribution to the collective behavior and gives out the overall system response as a result of all these influences.