Small-world scale-free brain graphs from EEG

Developing individualized spatial models that capture the complex dynamics of multi-electrode EEG data is essential for accurately decoding global neural activity. A widely used approach is network modeling, where electrodes are represented as nodes. A key challenge lies in defining the network edges and weights, as precise connectivity estimation is critical for enhancing neural characterization and extracting discriminative features, such as those needed for task decoding. Traditional EEG-derived brain graphs often fail to capture biologically grounded organizational principles such as small-world structure and heavy-tailed (scale-free) connectivity patterns. To address this gap, we introduce a framework for inferring subject-specific EEG-based brain graphs that explicitly designed to exhibit small-world and scale-free properties. Our approach begins by computing phase-locking values (PLV) between EEG channel pairs to build a backbone graph, which is then refined into an individualized small-world and scale-free network. To reduce computational complexity while preserving subject-specific characteristics, we apply Kron reduction to the resulting graph. Using two public EEG datasets, we evaluate the proposed method on motor imagery (MI) decoding and brain fingerprinting tasks. Our approach improves MI classification accuracy by 4-7% compared to conventional PLV, small-world, and scale-free graph models, and enhances differential identifiability in fingerprinting by 8-20% across six canonical frequency bands. These gains were statistically significant in both applications. Moreover, integrating graph signal processing features derived from our constructed graphs with classical EEG features further boosts performance. Overall, our findings highlight the potential of the proposed graph construction framework to enhance EEG analysis. By jointly capturing local segregation, global integration, and hub-driven hierarchical organization, the method strengthens downstream decoding and identification tasks, with promising implications for a wide range of applications in cognitive neuroscience and brain-computer interface research.