The brain most closely resembles a graph. See Marko's post on "Graphs, Brains, and Gremlin" (
http://markorodriguez.com/2011/07/14/graphs-brains-and-greml...).
Sebastian Seung is a leading researcher in the field of neuroscience called connectomics, which studies the wiring of the brain, and he is a professor at MIT's Department of Brain and Cognitive Sciences. He is focused on mapping the connections between each neuron and calls the mappings our "connectome," which he says is as individual as our genome.
He says scientists have hypothesized for years that each thought, each memory is stored as a neural connection. See his TED talk "I Am My Connectome" (http://www.ted.com/talks/lang/eng/sebastian_seung.html) and the Human Connectome Project (http://www.humanconnectomeproject.org).