Benefits of listening to music with emotional attachment while recovering from a cerebral ischemic event have been reported. To develop a better understanding of the effects of music listening on the human brain, an algorithm for the graph-theoretical analysis of functional magnetic resonance imaging (fMRI) data was developed. From BOLD data of two paradigms (block-design, first piece: music without emotional attachment, additional visual guidance by a moving cursor in the score sheet; second piece: music with emotional attachment), network graphs were constructed with correlations between signal time courses as edge weights. Functional subunits in these graphs were identified with the MCODE clustering algorithm and mapped back into anatomical space using AFNI. Emotional centers including the right amygdala and bilateral insula were activated by the second piece (emotional attachment) but not by the first piece. Network clustering analysis revealed two separate networks of small-world property corresponding to task-oriented and resting state conditions, respectively. Functional subunits with highest interactions were bilateral precuneus for the first piece and left middle frontal gyrus and right amygdala, bilateral insula, left middle temporal gyrus for the second piece. Our results indicate that fMRI in connection with graph theoretical network analysis is capable of identifying and differentiating functional subunits in the human brain when listening to music with and without emotional attachment.