Introducing the modularity graph: an application to brain functional networks

In signal processing, exploring complex systems through network representations has become an area of growing interest. This study introduces the modularity graph, a new graph-based feature, to highlight the relationship across the graph communities. After showing an application to the random graph class known as Stochastic Block Model, we consider the brain functional connectivity network estimated from real EEG data. The modularity graph provides a quantitative framework for examining the interactions between neuron clusters within the brain's network. The modularity graph works alongside multiscale community detection algorithms, thereby enabling the identification of community structures at various scales. After introducing the modularity graph, we apply it to the brain functional connectivity network, estimated from publicly available EEG recordings of motor imagery experiments. Statistical analysis across multiple scales shows that the modularity graph differs for the distinct brain connectivity states associated with various motor imagery tasks. This work emphasizes the application of signal on graph processing techniques to understand brain behavior during specific cognitive tasks, leveraging the novel modularity graph to identify patterns of brain connectivity in different cognitive conditions. This approach sets the stage for further signal on graph analysis to devise brain network modularity, and to gain insights into the motor imagery mechanisms.