Fibromyalgia (FM) is a chronic pain condition that is characterized by hypersensitivity to multi-modal sensory stimuli, widespread pain, and fatigue. We have previously proposed explosive synchronization (ES), a phenomenon wherein a small perturbation to a network can lead to an abrupt state transition, as a potential mechanism of the hypersensitive FM brain. Therefore, we hypothesized that converting a brain network from ES to general synchronization (GS) may reduce the hypersensitivity of FM brain. To find an effective brain network modulation to convert ES into GS, we constructed a large-scale brain network model near criticality (i.e., an optimally balanced state between order and disorders), which reflects brain dynamics in conscious wakefulness, and adjusted two parameters: local structural connectivity and signal randomness of target brain regions. The network sensitivity to global stimuli was compared between the brain networks before and after the modulation. We found that only increasing the local connectivity of hubs (nodes with intense connections) changes ES to GS, reducing the sensitivity, whereas other types of modulation such as decreasing local connectivity, increasing and decreasing signal randomness are not effective. This study would help to develop a network mechanism-based brain modulation method to reduce the hypersensitivity in FM.Author summaryPhase transitions, the physical processes of transition between system states in nature, are divided into two broad categories: first and second-order phase transitions. For example, boiling water presents abrupt transition (a first-order) along with high sensitivity to temperature change, distinct from gradual magnetization near Curie temperature (a second-order). Recently, we found that chronic pain shows specific brain network configurations that can induce the first-order transition, so-called ‘explosive synchronization.’ In this modeling study, we tried to identify a modulation method that can convert a first-order transition into a second-order transition in the brain network, expecting that it may inhibit the hypersensitivity in chronic pain. We found that increasing structural connectivity of hubs changes the type of phase transition in the brain network, significantly reducing network sensitivity.