The human connectome is a complex network that transmits information between interlinked brain regions. Using graph theory, previously well-known network measures of integration between brain regions have been constructed under the key assumption that information flows strictly along the shortest paths possible between two nodes. However, it is now apparent that information does flow through non-shortest paths in many real-world networks such as cellular networks, social networks, and the internet. In the current hypothesis, we present a novel framework using the maximum flow to quantify information flow along all possible paths within the brain, so as to implement an analogy to network traffic. We hypothesize that the connection strengths of brain networks represent a limit on the amount of information that can flow through the connections per unit of time. This allows us to compute the maximum amount of information flow between two brain regions along all possible paths. Using this novel framework of maximum flow, previous network topological measures are expanded to account for information flow through non-shortest paths. The most important advantage of the current approach using maximum flow is that it can integrate the weighted connectivity data in a way that better reflects the real information flow of the brain network. The current framework and its concept regarding maximum flow provides insight on how network structure shapes information flow in contrast to graph theory, and suggests future applications such as investigating structural and functional connectomes at a neuronal level.