The brain is expensive, incurring high material and metabolic costs for its size--relative to the size of the body--and many aspects of brain network organization can be mostly explained by a parsimonious drive to minimize these costs. However, brain networks or connectomes also have high topological efficiency, robustness, modularity and a 'rich club' of connector hubs. Many of these and other advantageous topological properties will probably entail a wiring-cost premium. We propose that brain organization is shaped by an economic trade-off between minimizing costs and allowing the emergence of adaptively valuable topological patterns of anatomical or functional connectivity between multiple neuronal populations. This process of negotiating, and re-negotiating, trade-offs between wiring cost and topological value continues over long (decades) and short (millisecond) timescales as brain networks evolve, grow and adapt to changing cognitive demands. An economical analysis of neuropsychiatric disorders highlights the vulnerability of the more costly elements of brain networks to pathological attack or abnormal development.