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Purpose: The objective of this research is to study and compare the coauthorship graphs (networks) of Iranian researchers in the main fields of mathematics by using records, extracted from WOS and Google Scholar, and graph parameters.

Methodology: The co-authorship graphs (networks) of Iranian researchers in 6 specialty fields of mathematics have been drawn by mathematical methods and software. Overall this research, 276 Iranian researchers in mathematics were considered and the co-authorship graphs in all fields were drawn and compared. Some mathematical graph parameters such as degrees of vertices, diameter, radius, independence number, vertex and edge chromatic numbers, matching number, for all co-authorship graphs were calculated too. Finally, we analyze and compare the co-authorship graphs by using these graph parameters. Findings: The research findings showed that two specialty fields Operation Research and Graphs and Combinatorics with average degrees 4.20 and 3.70, respectively, have high research collaboration with respect to other fields. The greatest diameter in the co-authorship graph, which equals 8, belongs to Commutative Algebra and the co-authorship graphs of the specialty field Numerical Analysis and Group Theory have the same least value of radius 3.

Conclustion: In some specialty fields of mathematics, which are pure, there is not enough collaboration among Iranian researchers. So, it is better that these researchers try to have more collaboration to publish stronger and deeper research works in the international journals. For this aim, more budget allocations should be considered to …