Graph Modularity and Randomness Measures : A Comparative Study

The human brain connectome exhibits a specific structure diagram that is understood to not be wired for randomness. However, aberrant connectivity has been detected and moreover linked to multiple neuropsychiatric and neurological diseases. Graph theory has provided a set of methods to evaluate disruption of brain structure organization. An alternative approach evaluates the difference between brain connectivity matrices and random matrices aiming at assessing randomness. This work compares both approaches within the context of random connectivity. Results indicate the correlation between the two assessments depends on the degree and can be as high as 0.3. Consequently, the two concepts can be treated as complementary, but addressing different aspects of randomness.