Brains in vivo appear to operate at the critical phase transition between ordered and 
disordered states, which leads to emergent spatio-temporal power-law correlations in 
brain dynamics and several functional benefits. 
While this phase transition is point-like in homogeneous systems, recent theoretical and 
experimental studies suggest that heterogeneity may stretch the critical point 
into an extended regime of critical-like dynamics, known as the Griffiths Phase (GP). 
GP in brain dynamics would allow the preservation of critical-like dynamics across a 
range of spontaneous or intentional shifts in control-parameter values, which would be 
catastrophic in homogeneous systems. 
It has, however, remained unclear, which forms of heterogeneity in the human structural 
connectome of white-matter connections constitute the predominant 
"heterogeneity control parameters" for GP per se. 
We addressed this question with computational modeling using a new Hierarchical Kuramoto 
approach and large-scale structural connectivity data from N = 230 subjects. 
We found the individual structural connectomes to endow individual subjects with widely 
different capacities to express emergent dynamics. 
In this presentation, I will address the relationships among GP width, nodal and global 
synchronizability, and the graph properties of the individual structural connectomes. 
These findings will be discussed in the context of neurophysiological and behavioural
functional implications.