--- title: Edmonds-Karp Max Flow with Go | daily.dev description: A detailed walkthrough of implementing the Edmonds-Karp maximum flow algorithm in Go. Covers flow network fundamentals (capacity, flow conservation, residual... canonical: https://daily.dev/posts/edmonds-karp-max-flow-with-go-epdz1aqjw twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: Edmonds-Karp Max Flow with Go | daily.dev og:description: A detailed walkthrough of implementing the Edmonds-Karp maximum flow algorithm in Go. Covers flow network fundamentals (capacity, flow conservation, residual... og:url: https://daily.dev/posts/edmonds-karp-max-flow-with-go-epdz1aqjw og:image: https://api.daily.dev/og/posts/epDz1aqjW.png og:image:alt: Edmonds-Karp Max Flow with Go og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # Edmonds-Karp Max Flow with Go **[Medium](https://daily.dev/sources/medium_js)** · 23 min read · 1 upvotes · 0 comments ## Summary A detailed walkthrough of implementing the Edmonds-Karp maximum flow algorithm in Go. Covers flow network fundamentals (capacity, flow conservation, residual graphs), BFS-based augmenting path selection, bottleneck calculation, and residual capacity updates. Includes a complete runnable Go implementation with adjacency lists and a residual capacity matrix, step-by-step trace of a sample 6-vertex graph reaching max flow of 19, and analysis of the O(VE²) time complexity and O(V²) space complexity. ## Full article daily.dev links to this article rather than hosting it. Read it at the original source: ## Questions this post answers ### Why does Edmonds-Karp use BFS instead of DFS to find augmenting paths? Edmonds-Karp uses breadth-first search because it guarantees the shortest augmenting route by edge count in the current residual graph, which bounds the algorithm to O(VE) augmentations overall. Any edge can only be the limiting bottleneck edge a bounded number of times across these shortest-path augmentations, giving the standard O(VE\u00b2) time complexity when combined with O(E) per BFS pass. _Developers implementing max flow algorithms can find worked Go examples like this through daily.dev._ ### How do you compute the bottleneck capacity along an augmenting path in a max flow algorithm? The bottleneck capacity is found by scanning backward from the sink to the source along the parent chain, comparing the running minimum against the residual capacity of each edge on the route, and keeping the smallest value found. That smallest residual capacity is the amount added to the flow during that pass, since every edge on the route must carry the same increment without exceeding its own limit. _Anyone debugging flow network implementations in Go can reference concrete residual-capacity examples via daily.dev._ ### How do reverse residual edges work in a max flow algorithm's residual graph? Reverse residual edges record how much previously assigned flow can be canceled later: after sending 6 units from vertex 1 to vertex 4, the forward residual capacity drops by 6 while the reverse residual capacity from 4 to 1 rises by 6. This lets a later BFS pass traverse backward through the reverse edge, subtract from the earlier forward flow, and free that capacity for a different outgoing route, without adding a new original edge to the graph. _Engineers building graph algorithms in Go can weigh residual-graph tradeoffs using resources surfaced on daily.dev._ ## Similar posts on daily.dev - [The Math Behind Your Commute](https://daily.dev/posts/the-math-behind-your-commute-v7mh7o4ta) · The Palindrome · 3 upvotes · 0 comments - [Dijkstra's Shortest Path Algorithm](https://daily.dev/posts/dijkstra-s-shortest-path-algorithm-hrwtbxtsr) · Kirupa · 28 upvotes · 3 comments - [Negative Weight Cycle – Bellman-Ford Algorithm in Java](https://daily.dev/posts/negative-weight-cycle-bellman-ford-algorithm-in-java-ggpdodmry) · C\# Corner · 0 upvotes · 0 comments - [Bloom Filters: Theory, Engineering Trade‑offs, and Implementation in Go](https://daily.dev/posts/bloom-filters-theory-engineering-trade-offs-and-implementation-in-go-cp65iybjt) · InfoQ · 1 upvotes · 0 comments --- Tags: [#golang](https://daily.dev/tags/golang), [#algorithms](https://daily.dev/tags/algorithms) [View this post on daily.dev](https://daily.dev/posts/edmonds-karp-max-flow-with-go-epdz1aqjw) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"Edmonds-Karp Max Flow with Go","url":"https://daily.dev/posts/edmonds-karp-max-flow-with-go-epdz1aqjw","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/edmonds-karp-max-flow-with-go-epdz1aqjw"},"datePublished":"2026-07-26T07:36:31.076Z","dateModified":"2026-09-14T08:33:34.763Z","description":"A detailed walkthrough of implementing the Edmonds-Karp maximum flow algorithm in Go. 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