The growth and evolution of domain knowledge have always been the focus of Library and Information Science. Exploring the emergence of correlations in the process of knowledge growth with network science thinking can reveal the growth patterns and mechanisms of knowledge correlations. The present research extracts a total of over 440 000 pairs of knowledge correlations, 870 000 times of correlation frequency, which are divided into 11 time windows. The small world and scale free properties of time series domain knowledge network topology are determined by the short average path length, the high clustering coefficient and the power law distribution of degree. On this basis, the knowledge correlations and frequencies in the process of domain knowledge growth are tracked and analyzed from the aspects of the number of correlation frequencies, the proportion of correlation frequencies, the status of neighboring windows, etc.
Results have shown that in the process of knowledge correlation growth, the frequency distribution of correlations is in accordance with power law. Through the time series analysis of the frequency of knowledge correlations, it is found that the frequency distribution of knowledge correlations in the same network can better fit the power law than the degree distribution of nodes, without the phenomenon of “top heavy distribution” usually found in the degree distribution of nodes, and the power law distribution of the frequency of knowledge correlations performs better in the latter part of the time series. This phenomenon shows that although the knowledge correlations determine the topology of knowledge networks, only a few correlations have extremely high frequency values, while most of them have only a small number of frequency values, and the process of frequency of knowledge correlations is that of frequency emergence. On the other hand, the growth process of knowledge correlations has the property of “the rich gets richer” in frequency, and mainly follows the mechanism of “preferential reinforcement”. 
Statistics show that as the frequency of knowledge correlations grows and accumulates, the few frequency “rich” (high frequency correlation) occupy more and more frequency “wealth” than most frequency “poor” (low frequency correlation). The gap between the “rich” and the “poor” in frequency of knowledge correlations becomes more and more obvious in the second half of the timeline as the domain knowledge grows and develops. The status of the neighboring windows shows that most of the knowledge correlations in the frequency “extremely rich” status often have the “extremely rich” status in the previous time window. Correlations with more frequency “wealth” will attract additional frequencies with a higher probability in the process of growth and development of domain knowledge, reflecting the frequency growth mechanism of “preferential reinforcement”. The repeated superimposition of the micro rules of “preferential reinforcement” on the time series have created the phenomena of “the rich get richer” at the frequency level in the emergence of correlation. The study has also found the “bursts reinforcement” phenomenon that the correlations in frequency “extremely poor” status suddenly jump into the “extremely rich” status. The main reason for this phenomenon is that academia has produced significant findings or inventions, which provide a possibility for identifying significant academic achievements based on the frequency of knowledge correlation.
Although the knowledge networks based on social tagging system used in this study are not comprehensive to cover all types of knowledge networks, the emergence patterns and mechanisms of knowledge correlation based on frequency evolution help to promote research in knowledge networks and knowledge growth, and they also benefit studies on social networks, communication networks, transport networks, etc. 5 figs. 4 tabs. 30 refs.