Academic collaboration (co-authorship) networks are networks of researchers working together on the same or different disciplines. These networks are used in areas such as the analysis of the development of a country, the ranking of universities and departments. At the same time, the modeling of academic collaborations and the conclusions and interpretations to be made at the level of collaborations through these models are also of great importance. Since this important topic has not been mathematically modeled, the collaboration graphs have been proposed as a new graph type and the related definitions and algorithms have been presented. The academic collaborations in Turkey are modeled with the new graph type presented. The data used in the modeling was extracted from the Web of Science (WOS) database with an application developed and saved as relational database format. The application covers studies that have been published between 1980 and 2015 (including end points) those have authors studying in institutions of Turkey. The main motivation in choosing this data as modeling data is that such a comprehensive study on Turkey has not been done yet. Turkey's academic collaborations are modeled on a regional basis, using the data obtained and the type of graph proposed. A statistical Bron-Kerbosch (iBK) algorithm was developed based on the Bron-Kerbosch (BK) algorithm. The community detection was done using both algorithms. Outputs of algorithms compared. In the light of the results obtained, conclusions were made about the factors affecting the academic collaborations in Turkey.