Modern network science has revealed fundamental aspects of normal brain-network organization, such as small-world and scale-free patterns, hierarchical modularity, hubs and rich clubs. The next challenge is to use this knowledge to gain a better understanding of brain disease. Recent developments in the application of network science to conditions such as Alzheimer's disease, multiple sclerosis, traumatic brain injury and epilepsy have challenged the classical concept of neurological disorders being either 'local' or 'global', and have pointed to the overload and failure of hubs as a possible final common pathway in neurological disorders.