Criticality has been conjectured as an integral part of neuronal network dynamics. Operating at a critical threshold requires precise parameter tuning and a corresponding mechanism remains an open question. Recent studies have suggested that topological features observed in brain networks give rise to a Griffiths phase, leading to power-law scaling in brain activity dynamics and the operational benefits of criticality in an extended parameter region. Motivated by growing evidence of neural

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... lates of different states of consciousness, we investigate how topological changes affect the expression of a Griffiths phase. We analyze the activity decay in modular networks using a susceptible-infected-susceptible propagation model and find that we can control the extension of the Griffiths phase by altering intra-and intermodular connectivity. We find that by adjusting system parameters, we can counteract changes in critical behavior and maintain a stable critical region despite changes in network topology. Our results give insight into how structural network properties affect the emergence of a Griffiths phase and how its features are linked to established topological network metrics. We discuss how those findings could contribute to an understanding of the changes in functional brain networks.