Individuality, the uniqueness that distinguishes one person from another, may manifest as diverse rearrangements of functional connectivity during heterogeneous cognitive demands; yet, the neurobiological substrates of individuality, reflected in inter-individual variations of large-scale functional connectivity, have not been fully evidenced. Accordingly, we explored inter-individual variations of functional connectivity dynamics, subnetwork patterns and modular architecture while subjects watched identical video clips designed to induce different arousal levels. How inter-individual variations are manifested in the functional brain networks was examined with respect to four contrasting divisions: edges within the anterior versus posterior part of the brain, edges with versus without corresponding anatomically-defined structural pathways, inter- versus intra-module connections, and rich club edge types. Inter-subject variation in dynamic functional connectivity occurred to a greater degree within edges localized to anterior rather than posterior brain regions, without adhering to structural connectivity, between modules as opposed to within modules, and in weak-tie local edges rather than strong-tie rich-club edges. Arousal level significantly modulates inter-subject variability in functional connectivity, edge patterns, and modularity, and particularly enhances the synchrony of rich-club edges. These results imply that individuality resides in the dynamic reconfiguration of large-scale brain networks in response to a stream of cognitive demands.