The science of connectomics
The scientific study of connectomics involves mapping out the detailed connectivity of brain regions to characterize the architectural networks of the human brain. Connectomics is therefore a powerful tool to visualize the structural and functional dysconnections associated with schizophrenia. The human connectome provides a detailed map of brain-wide circuit connectivity and allows inference into how brain function may be affected by disruption of the structural organizational network (31, 34). At the micro-scale, the physical wiring of single neurons and their synaptic connections to other neurons through dendritic and axonal connections comprise local network circuits. At the meso-scale (local populations of 80–100 neurons that span all cortical layers), connectivity is at the level of functionally specialized subnetworks within single cortical columns that are selectively connected within and between neighboring cortical columns and constitute a major functional element for cortical information processing. At the macro-scale, inter-regional connectivity of cerebral lobes via WM interhemispheric tracts is responsible for the integration and relay of information between various parts of the brain (34).
Connectomics heavily utilizes graph theory, a specialized discipline of mathematics concerned with the study of graphs or models that represent relations between objects. Large collections of algorithms are used to calculate topological characteristics of both structural and functional brain imaging connectivity data that can be represented in the form of a graph. The graph consists of nodes that represent single neurons or brain regions that are defined by connection endpoints of two line segments that are then linked by edges that illustrate their direct connection to each other via axonal projections, WM pathways or functional coupling between inter-regional brain areas (31). The closeness of neuronal and brain region nodes represents a higher probability of being connected, as long axonal projections are functionally expensive in terms of wiring costs. The tendency of nodes to cluster and form shorter communication paths allows for more efficient integration between spatially disconnected node pairs. The degree or number of edges each node possesses and how close they are to each other (centrality) represents the interconnectivity of a node to other nodes within the entire brain network. Nodes that have a high degree of edges and possess high centrality are known as hubs (35–37). In turn, brain hubs that are “rich” in connectivity and more densely interconnected to each other in comparison to what their high degree alone would predict form a central “rich club organization” essential for the integration of global information and brain communication (37) as illustrated in Figure 1. Disruption to central “rich club” hubs of the human connectome has been associated with several brain disorders (38). Notably, hub lesions that are highly concentrated within cortical hubs of the frontal and temporal lobes are found to be specifically affected in schizophrenia (38).
Figure 1  Topological graph features of the connectome. (A) The graph consists of “nodes” that represent single neurons or brain regions and are linked by “edges” illustrating their connection to each other via axonal projections. (B) The “degree” or number of edges and how close they are to each other “centrality” represents the interconnectivity of nodes. (C) Nodes having a high degree of edges and high centrality are knowns as “hubs.” Brain hubs “rich” in connectivity to each other and found centrally form the “rich club organization.” The rich club hubs found in cortical and frontal lobe regions of the brain are affected in schizophrenia.