There are many ways to measure the graph cohesiveness in respect of different graph attributes. For our purposes we were looking for a measure that accounts for overall graph connectivity of the CG since actual scientific concepts tend to have more citations than common phrases, i.e., the CGs (Citation Graph) of scientific concepts tend to be more connected. Such a measure was conveniently provided by the Beta index which measures the level of connectivity in a graph and is expressed by the relationships between number of edges over the numbers of nodes (Eq. 1). The tree graphs have a Beta index of less than 1. A graph with a single cycle has a Beta value of 1 and more complex networks have a higher value of Beta index. To evaluate the emergence of scientific topics we took a closer look at the distributions of publications and citations over the years (Figure ). While publications themselves are regarded as a way to establish a research topic, the number of citations is usually considered as a better measure of the impact the topic has in the scientific community. In our study we make a distinction between two types of citations. As a "regular citation" (or just citation) we regarded a document that contains the phrase and cites another document that also contains the phrase. As an "extra citation" we considered a document that does not contain the phrase and cited a document that contains the phrase. One good measure for emergence would be to calculate the rate of increase/decrease of the publications/citations over a certain time limit. While it is possible to take the actual number of publications/citations over a given period and calculate the corresponding rates, this may provide inconsistent results in case of unusual yearly fluctuations in the data. To mitigate this issue previous investigations used average values over several years. This helps to a certain degree but not enough to smoothen all data inconsistencies. To account for data fluctuations, instead of averaging the data, in our method, we use the actual yearly data distributions of publications/citations to fit a mathematical function that accurately approximates the observed data. We examined a few distinct functions such as sigmoid, gaussian, exponential, and polynomial with the best approximations obtained using a quartic polynomial function (Figure ) for our dataset. Using the derived mathematical function gives us a better solution to the data fluctuations problem and allows us to make predictions and, most importantly, to introduce our measure of emergence. As a measure of emergence, we define the slope of the curve of the mathematical function at the point of interest, i.e., the first derivative of the function. Figure illustrates the measures of emergence for publications, citations, and extra citations of the example phrase ("metal-organic framework") at year 2014.