Flow in Networks

Graph Theory · Axiom Academy

INTRO Introduction to Network Flow Watch how resources move through networks, from water in pipes to data on the internet! Imagine water flowing through a pipe system. The source (water tank) sends water, and the sink (destination) receives it. Adjust the flow rate to see how much water can move through the system! Each pipe has a maximum capacity . What happens when you try to push more water than a pipe can handle? Watch the bottleneck form! What if there are multiple paths from source to sink? The flow can split and take different routes! Adjust how much flow goes through each path. Network Flow in the Real World Flow networks appear everywhere! Click on each example to see how the same mathematical concept applies to different systems. A flow network consists of: (1) a source node that generates flow, (2) a sink node that consumes flow, (3) intermediate nodes where flow is conserved, and (4) edges with capacity constraints that carry flow. Capacity constraints: Flow on each edge cannot exceed its capacity. Flow conservation: For all nodes except source and sink, incoming flow equals outgoing flow. Maximum flow: The goal is often to find the maximum amount that can flow from source to sink. You'll learn powerful algorithms like Ford-Fulkerson and Edmonds-Karp that find maximum flows efficiently. You'll discover the Max-Flow Min-Cut theorem , explore bipartite matching , and see how these concepts solve real optimization problems in networks!

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