Before revision:  A few measures of information flow have been proposed previously in the literature, and measures of directed causal influence are currently being used as a heuristic proxy for information flow. However, there is as yet no rigorous treatment of the problem with formal definitions and clearly stated assumptions, and the process of defining information flow is often conflated with the problem of estimating it. In this work, we provide a new information-theoretic definition for information flow in a computational system, which we motivate using a series of examples.
After revision:  We are interested in a definition that captures the dynamic flow of information about a specific message, and which guarantees an unbroken "information path" between appropriately defined inputs and outputs in the directed graph. Prior measures, including those based on Granger Causality and Directed Information, fail to provide clear assumptions and guarantees about when they correctly reflect information flow about a message. We take a systematic approach---iterating through candidate definitions and counterexamples---to arrive at a definition for information flow in a computational system, which we motivate using a series of examples.