The brain is made up of billions of neurons that form an intricate graph of connections. A connectome is a comprehensive map of connections within a given system. In the field of neuroscience, connectomics, or brain connectivity network analysis, provides a tool with which we can capture and model the evolution of brain networks.
A structural connectome describes the network of anatomical links (i.e. axonal projections) throughout the brain. A functional connectome describes the statistical correlation of activity between different areas of the brain (regardless of whether or not they’re structurally connected). An effective connectome describes the causal influence that each area of the brain exerts on the activity of other areas.
I recently came across the following video which does a great job at explaining connectomes to different audiences: