The perception of physical exertion is the cognitive sensation of work demands associated with voluntary muscular actions. Measurements of exerted force are crucial for avoiding the risk of overexertion and understanding human physical capability. For this purpose, various physiological measures have been used; however, the state-of-the-art in-force exertion evaluation lacks assessments of underlying neurophysiological signals. The current study applied a graph theoretical approach to investigate the topological changes in the functional brain network induced by predefined force exertion levels for twelve female participants during an isometric arm task and rated their perceived physical comfort levels. The functional connectivity under predefined force exertion levels was assessed using the coherence method for 84 anatomical brain regions of interest at the electroencephalogram (EEG) source level. Then, graph measures were calculated to quantify the network topology for two frequency bands. The results showed that high-level force exertions are associated with brain networks characterized by more significant clustering coefficients (6%), greater modularity (5%), higher global efficiency (9%), and less distance synchronization (25%) under alpha coherence. This study on the neurophysiological basis of physical exertions with various force levels suggests that brain regions communicate and cooperate higher when muscle force exertions increase to meet the demands of physically challenging tasks.