Studying Functional Brain Networks to Understand Mathematical Thinking: A Graph-Theoretical Approach

Brain function during mathematical thinking is a common concern of scientists from different research fields. The study of functional brain networks extracted from electroencephalographic (EEG) signals using graph theory seems to meet the challenge of neuroscience to understand brain functioning in terms of dynamic flow of information among brain regions. Some studies have found differences between the basic arithmetic operations among brain regions; however, they have not explained the brain function during difficult mathematical tasks and complex mathematical processing. This study investigates the changes of the functional networks’ organization among different mathematical tasks. To this end, EEG data from 10 subjects were recorded during three different tasks, Number Looking which was served as the control situation, Simple Addition which refers to the addition of single-digit numbers and Difficult Multiplication with trials of two-digit multiplications. We analyzed weighted graphs so as to provide a more realistic representation of functional brain networks. Mutual information was employed to form the weights among the different channels, while various global and local graph indices were further examined. The results suggest that there are some statistically significant differences between graph theoretical indices among the different tasks and their range of values depend on the particular task.