Despite many decades of study, scientists still puzzle over the process of insight. By what mechanism does a person experience that "Aha!" moment, when sudden clarity emerges from a tangled web of thoughts and ideas? This research integrates psychological work on insight with graph theoretic work on "small-world" phenomenon, to construct a theory that explains how insight occurs, how it is similar to and different from more typical learning processes, and why it yields an affective response in the individual. I propose that cognitive insight occurs when an atypical association, forged through random recombination or directed search, results in a "shortcut" in an individual's network of representations. This causes a rapid decrease in path length, reorients the individual's understanding of the relationships within and among the affected representations, and can prompt a cascade of other connections. This result is demonstrated by applying graph theoretical analysis to network translations of commonly used insight problems.
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