Synchronisation of clusters around brain hubs promotes multiscale phase oscillations in the human connectome

Brain imaging data mapping onto human connectome networks enables the investigation of global brain dynamics, where the central brain regions known as brain hubs play an essential role in transferring activity between different brain parts. At this scale, the synchronisation processes are increasingly investigated as one of the key mechanisms revealing many aspects of brain functional coherence in healthy brains and revealing deviations due to various brain disorders. For the human connectome core network, consisting of the eight brain hubs and the higher-order structure attached to them, previous simulations of Kuramoto phase oscillators at network nodes indicate instability of the global order parameter for a range of positive coupling strengths. Focusing on this range of couplings, here we investigate the occurrence of the cluster synchronisation phenomenon in the human connectome core network and its manifestation in the multiscale temporal oscillations of the global phase order parameter. We use the spectral graph analysis and eigenvector localisation methodology, where the clusters of nodes playing a similar role in the synchronisation processes are identified via a small mutual distance in the eigenvector space. We determine three significant clusters of brain regions and show the position of hubs in them. With the parallel analysis of the weighted core network and its binary version, we demonstrate the primary role of the network’s topology in the formation of synchronised clusters. Meanwhile, the weights of edges contribute to the hub’s synchronisation with the surrounding cluster, stabilise the order parameter variations and reduce the multifractal spectrum.