This study investigated how attending to auditory and visual information systematically changes graph theoretical measures of integration and functional connectivity between three network modules: auditory, visual, and a joint task core. Functional MRI BOLD activity was recorded while healthy volunteers attended to colour and/or pitch information presented within an audiovisual stimulus sequence. Network nodes and modules were based on peak voxels of BOLD contrasts, including colour and pitch sensitive brain regions as well as the dorsal attention network. Network edges represented correlations between nodes' activity and were computed separately for each condition. Connection strength was increased between the task and the visual module when participants attended to colour, and between the task and the auditory module when they attended to pitch. Moreover, several nodal graph measures showed consistent changes to attentional modulation in form of stronger integration of sensory regions in response to attention. Together, these findings corroborate dynamical adjustments of both modality-specific and modality-independent functional brain networks in response to task demands and their representation in graph theoretical measures.