Several anatomical studies have identified specific anatomical features within the peri-sylvian brain system of absolute pitch (AP) musicians. In this study we used graph theoretical analysis of cortical thickness covariations (as indirect indicator of connectivity) to examine whether AP musicians differ from relative pitch musicians and nonmusicians in small-world network characteristics. We measured “local connectedness” (local clustering = γ), “global efficiency of information transfer” (path length = λ), “small-worldness” (σ = γ/λ), and “degree” centrality as measures of connectivity. Although all groups demonstrated typical small-world features, AP musicians showed significant small-world alterations. “Degree” as a measure of interconnectedness was globally significantly decreased in AP musicians. These differences let us suggest that AP musicians demonstrate diminished neural integration (less connections) among distant brain regions. In addition, AP musicians demonstrated significantly increased local connectivity in peri-sylvian language areas of which the planum temporale, planum polare, Heschl's gyrus, lateral aspect of the superior temporal gyrus, STS, pars triangularis, and pars opercularis were hub regions. All of these brain areas are known to be involved in higher-order auditory processing, working or semantic memory processes. Taken together, whereas AP musicians demonstrate decreased global interconnectedness, the local connectedness in peri-sylvian brain areas is significantly higher than for relative pitch musicians and nonmusicians.