--- title: Graph Algorithms description: This topic focuses on methods for traversing, searching, and analyzing network structures represented as vertices and edges. Learners will understand how to solve practical problems like finding the shortest path, detecting cycles, and modeling connectivity. category: programming-tech subcategory: algorithms-and-data-structures difficulty: beginner, intermediate, advanced url: /subject/graph-algorithms --- # Graph Algorithms This topic focuses on methods for traversing, searching, and analyzing network structures represented as vertices and edges. Learners will understand how to solve practical problems like finding the shortest path, detecting cycles, and modeling connectivity. ## Available Resources 1 Books • 6 Courses • 6 Websites ## Websites ### 1. CP-Algorithms - Minimum-cost flow (successive shortest path) Article explaining the successive shortest path algorithm for minimum-cost flow, an extension of Edmonds-Karp that augments along cheapest paths, covering directed and undirected graphs, complexity analysis, an SPFA-based implementation, and practice problems. Readers can implement min-cost max-flow for contest problems. **Difficulty:** Advanced | **Price:** Free **Link:** https://cp-algorithms.com/graph/min_cost_flow.html **Tags:** min-cost-flow, network-flow, shortest-paths, graph-algorithms, competitive-programming ### 2. Visualgo.net Interactive visualization module from VisuAlgo, built at the National University of Singapore, showing how graphs are stored as adjacency matrices, adjacency lists and edge lists, so learners can compare these representations and trace graph operations step by step. **Difficulty:** Beginner | **Price:** Free **Link:** https://visualgo.net/en/graphds **Tags:** graph-representation, adjacency-list, adjacency-matrix, data-structures, algorithm-visualization ### 3. GeeksforGeeks Graphs Tutorials and problems **Difficulty:** Beginner | **Price:** Free **Link:** https://www.geeksforgeeks.org/graph-data-structure-and-algorithms/ ### 4. Introduction to the A* Algorithm (Red Blob Games) **Author:** Amit J. Patel Amit Patel's interactive walkthrough builds breadth-first search up into Dijkstra's algorithm, greedy best-first search and A*, animating how each frontier expands across a grid so the tradeoffs between them are visible rather than asserted. **Difficulty:** Beginner | **Language:** English | **Price:** Free **Link:** https://www.redblobgames.com/pathfinding/a-star/introduction.html **Tags:** a-star, pathfinding, dijkstra, breadth-first-search, heuristic-search ### 5. visualgo.net Visualgo.net is an interactive visualization platform for learning data structures and algorithms, offering animated, step-by-step demonstrations of core structures (arrays, lists, stacks, queues, trees, graphs) and algorithms with explanations. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://visualgo.net **Tags:** websites, technology-computer-science, algorithms ### 6. LeetCode Online judge with thousands of algorithm and data-structure problems sorted by difficulty, topic and company, plus timed contests, discussion threads and study plans. Regular practice builds fluency with common interview problem patterns and writing correct, efficient code under time pressure. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://leetcode.com **Tags:** coding-interviews, algorithm-practice, data-structures, online-judge, problem-patterns ## Courses ### 1. Algorithmic Thinking (Part 1) **Author:** Luay Nakhleh, Scott Rixner, Joe Warren Rice University course on analysing algorithmic efficiency and applying it to graph problems. Students implement several graph algorithms in Python and use them to analyse two large real-world data sets, learning how the structure of data affects algorithm behaviour. **Difficulty:** Intermediate | **Price:** Free **Link:** https://www.coursera.org/learn/algorithmic-thinking-1 **Tags:** algorithmic-thinking, graph-algorithms, algorithm-efficiency, python ### 2. Introduction to Algorithms (MIT 6.006) **Author:** Erik Demaine, Jason Ku, Justin Solomon Modeling computational problems and solving them with core algorithms and data structures: sorting, hashing, binary trees, heaps, graph search, shortest paths and dynamic programming. 32 lecture videos, notes, problem sets and exams with solutions teach asymptotic analysis and algorithm design. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-spring-2020/ **Tags:** data-structures, asymptotic-analysis, graph-algorithms, dynamic-programming, sorting ### 3. Trees and Graphs: Basics **Author:** Sriram Sankaranarayanan University of Colorado Boulder course covering binary search trees, balanced trees, graph traversals, union-find, minimum spanning trees, and shortest-path algorithms, with Python programming assignments. Finishing it, you can implement and reason about the cost of these structures. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.coursera.org/learn/trees-graphs-basics **Tags:** graph-algorithms, graph-traversal, shortest-paths, minimum-spanning-trees, union-find, binary-search-trees ### 4. Algorithms, Part I This course covers the essential information that every serious programmer needs to know about algorithms and data structures, with emphasis on applications and scientific performance analysis of Java implementations. Part I covers elementary data structures, sorting, and searching algorithms. Part II focuses on graph- and string-processing algorithms. All the features of this course are available for free. People who are interested in digging deeper into the content may wish to obtain the textbook Algorithms, Fourth Edition (upon which the course is based) or visit the website algs4.cs.princeton.edu for a wealth of additional material. This course does not offer a certificate upon completion. **Difficulty:** Beginner | **Language:** English | **Duration:** 6 weeks of study, 6–10 hours per week. | **Price:** Free **Link:** https://www.coursera.org/learn/algorithms-part1 **Tags:** courses, technology-computer-science, algorithms ### 5. Algorithms, Part II This course covers the essential information that every serious programmer needs to know about algorithms and data structures, with emphasis on applications and scientific performance analysis of Java implementations. Part I covers elementary data structures, sorting, and searching algorithms. Part II focuses on graph- and string-processing algorithms. All the features of this course are available for free. People who are interested in digging deeper into the content may wish to obtain the textbook Algorithms, Fourth Edition (upon which the course is based) or visit the website algs4.cs.princeton.edu for a wealth of additional material. This course does not offer a certificate upon completion. **Difficulty:** Beginner | **Language:** English | **Duration:** 6 weeks of study, 6–10 hours per week. | **Price:** Free **Link:** https://www.coursera.org/learn/algorithms-part2 **Tags:** courses, technology-computer-science, algorithms ### 6. Advanced Graph Algorithms Strengthen your skills in algorithmics and graph theory, and gain experience in programming in Python along the way. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://www.edx.org/learn/python/imt-advanced-algorithmics-and-graph-theory-with-python **Tags:** courses, technology-computer-science, algorithms ## Books ### 1. Graph Algorithms **Author:** Shimon Even Classic 1979 text on graph algorithms covering shortest paths, trees, depth-first and breadth-first search, network flows and their applications, and planarity testing, giving readers a rigorous grounding in the design and correctness proofs of core graph algorithms. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0914894218?tag=edmonddante07-20 **Tags:** books, technology-computer-science, algorithms --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/graph-algorithms