Well-established structural abnormalities, mostly involving the limbic system, have been associated with disorders of emotion regulation. Understanding the arrangement and connections of these regions with other functionally specialized cortico-subcortical subnetworks is key to understanding how the human brain's architecture underpins abnormalities of mood and emotion. We investigated topological patterns in bipolar disorder (BD) with the anatomically improved precision conferred by combining subject-specific parcellation/segmentation with non-tensor based tractograms derived using a high-angular resolution diffusion-weighted approach. Connectivity matrices were constructed using 34-cortical and 9-subcortical bilateral nodes (Desikan-Killiany) and edges that were weighted by fractional anisotropy and streamline count derived from deterministic tractography using constrained spherical deconvolution. Whole-brain and rich-club connectivity alongside a permutation-based statistical approach were employed to investigate topological variance in predominantly euthymic BD relative to healthy volunteers. Bipolar disorder patients (n=40) demonstrated impairments across whole-brain topological arrangements (density, degree, and efficiency), and a dysconnected subnetwork involving limbic and basal ganglia relative to controls (n=45). Increased rich-club connectivity was most evident in females with BD, with fronto-limbic and parieto-occipital nodes not members of BD rich-club. Increased centrality in females relative to males was driven by basal ganglia and fronto-temporo-limbic nodes. Our subject-specific cortico-subcortical non-tensor-based connectome map presents a neuroanatomical model of BD dysconnectivity that differentially involves communication within and between emotion-regulatory and reward-related subsystems. Moreover, the female brain positions more dependence on nodes belonging to these two differently specialised subsystems for communication relative to males, which may confer increased susceptibility to processes dependent on integration of emotion and reward-related information.