Graph attention-guided dynamics for adaptive community evolution in complex networks

Abstract

We propose an adaptive framework for community detection in complex networks by integrating coupled Rössler oscillators with graph neural network embeddings. Oscillator coupling strengths are modulated by node similarities learned through a graph convolutional network (GCN) with orthogonalized embeddings, refined via a graph attention network (GAT) mechanism. At periodic intervals, a feature matrix combining oscillator states, frequencies, phases, and graph metrics is processed through a three-layer GCN with a composite loss balancing kernel -means clustering, spectral alignment via an adaptively fused Laplacian, and adjacency reconstruction. The resulting embeddings are clustered to reveal mesoscale community structure. The reconstructed adjacency modulates coupling via elementwise multiplication with the original graph, row-normalization, and a hyperbolic tangent activation, while oscillator frequencies update to the median of neighbors, promoting intra-community synchronization. The framework is validated on four benchmark networks, Karate, Dolphins, Jazz, and Football, spanning different sizes and structural complexities. Results are compared against established methods, including Joint Spectral Clustering, Spectral Clustering, and Walktrap. Modularity (Q) and Normalized Mutual Information (NMI) are evaluated across multiple community resolutions, revealing hierarchical structures consistent with prior literature. The proposed method achieves competitive modularity across all networks, with perfect agreement with ground truth on the Karate network (NMI=1.0) and a near perfect NMI of 0.9025 on the Football network, surpassing state of the art results. By capturing meaningful community structures at different granularities, the framework offers a principled, data driven pathway to study community formation in physical, biological, and engineered networks.