Network inhomogeneities can strongly affect the critical dynamics of spreading models if the graph dimension is finite, causing large fluctuations and nonuniversal power-laws in extended control parameter spaces. This provides an alternative or an extension of self-organized criticality, observed in nature very frequently. These Griffiths Effects (GE) are generated by rare-regions and can be observed even in finite scale-free graphs. Real networks are very often modular, that may enhance GE-s and may lead to true  Griffiths phases, where the

fluctuations diverge. Participation in the research of GE-s in various network models with large scale simulations or by other methods would be the target of this topic. Besides spreading models we plan to study synchronisation transitions from this point of view with a special emphasis on brain and power-grid models.