Graph Algorithms Last Updated : 21 Jun, 2025 Summarize Comments Improve Suggest changes Share Like Article Like Report Graph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social network, a computer network, a network of locations used in GPS and many more examples where different nodes or vertices are connected without any hierarchic or constraint on structure.BasicsGraph and its representationsBFS and DFS Breadth First TraversalDepth First Traversal Difference between BFS and DFSRotten TomatoesIslands in a GraphFlood FillCheck for BipartiteWord Ladder Snakes and LadderWater Jug problemPacific Atlantic Water FlowShortest Path in Binary MatrixClone a Graph Transitive Closure of a Graph using DFSCycles Cycle in a Directed GraphCycle in an undirected graphCycle in a graph using colorsNegative cycle in a Graph | (Bellman Ford)Cycles of length nClone a Directed Acyclic Graph Disjoint Set Data Structure or Union-Find AlgorithmShortest Path Dijkstra’s shortest path aBellman–Ford Floyd Warshall Johnson’s algorithm Shortest Path in Directed Acyclic GraphDial’s AlgorithmMultistage Graph (Shortest Path)Shortest path in an unweighted graphMinimum mean weight cycle algorithm0-1 BFS (Shortest PathMinimum weight cycle D’Esopo-Pape AlgorithmMinimum Spanning TreePrim’s Minimum Spanning Tree (MST)Kruskal’s Minimum Spanning Tree Prim’s vs Kruskal’s algorithm for MSTApplications of Minimum Spanning Tree ProblemMinimum cost to connect all citiesTotal number of Spanning Trees in a GraphMinimum Product Spanning TreeReverse Delete Algorithm for Minimum Spanning TreeBoruvka’s algorithm for Minimum Spanning TreeTopological SortingTopological SortingAll topological sorts of a Directed Acyclic GraphKahn’s Algorithm for Topological SortingMaximum edges that can be added to DAG so that is remains DAGLongest Path in a Directed Acyclic GraphTopological Sort of a graph using departure time of vertexFind Itinerary from a given list of ticketsConnectivity in GraphArticulation Points (or Cut Vertices) in a GraphBiconnected ComponentsBridges in a graphEulerian path and circuitFleury’s Algorithm for printing Eulerian Path or CircuitStrongly Connected ComponentsCount all possible walks from a source to a destination with exactly k edgesEuler Circuit in a Directed GraphLength of shortest chain to reach the target wordFind if an array of strings can be chained to form a circleTarjan’s Algorithm to find strongly connected ComponentsPaths to travel each nodes using each edge (Seven Bridges of Königsberg)Dynamic Connectivity | Set 1 (Incremental)Maximum Flow in GraphMax Flow Problem IntroductionFord-Fulkerson Algorithm for Maximum Flow ProblemFind maximum number of edge disjoint paths between two verticesFind minimum s-t cut in a flow networkMaximum Bipartite MatchingChannel Assignment ProblemIntroduction to Push Relabel AlgorithmKarger’s Algorithm- Set 1- Introduction and ImplementationDinic’s algorithm for Maximum FlowSome must do Problems Find length of the largest region in Boolean MatrixCount number of trees in a forestA Peterson Graph ProblemClone an Undirected GraphGraph Coloring (Introduction and Applications)Traveling Salesman Problem (TSP) ImplementationVertex Cover Problem | Set 1 (Introduction and Approximate Algorithm)K Centers Problem | Set 1 (Greedy Approximate Algorithm)Erdos Renyl Model (for generating Random Graphs)Chinese Postman or Route Inspection | Set 1 (introduction)Hierholzer’s Algorithm for directed graphCheck whether a given graph is Bipartite or notSnake and Ladder ProblemBoggle (Find all possible words in a board of characters)Hopcroft Karp Algorithm for Maximum Matching-IntroductionMinimum Time to rot all orangesConstruct a graph from given degrees of all verticesDetermine whether a universal sink exists in a directed graphNumber of sink nodes in a graphTwo Clique Problem (Check if Graph can be divided in two Cliques)If you are looking for difficulty-wise list of problems, please refer to Graph Data Structure.Some QuizzesQuizzes on Graph TraversalQuizzes on Graph Shortest PathQuizzes on Graph Minimum Spanning TreeQuizzes on GraphsQuick Links :Top 10 Interview Questions on Depth First Search (DFS)Some interesting shortest path questionsPractice Problems on Graphs Recommended:Learn Data Structure and Algorithms | DSA Tutorial Introduction to Graph Visit Course Introduction to Graph Graph Representation (Adjacency Matrix) Graph Representation (Adjacency List) GRAPH Data Structure | What is Graph? | DSA Course Comment More infoAdvertise with us Next Article Dynamic Programming or DP H harendrakumar123 Follow Improve Article Tags : Graph DSA Practice Tags : Graph Similar Reads DSA Tutorial - Learn Data Structures and Algorithms DSA (Data Structures and Algorithms) is the study of organizing data efficiently using data structures like arrays, stacks, and trees, paired with step-by-step procedures (or algorithms) to solve problems effectively. Data structures manage how data is stored and accessed, while algorithms focus on 7 min read Basics & PrerequisitesTime Complexity and Space ComplexityMany times there are more than one ways to solve a problem with different algorithms and we need a way to compare multiple ways. Also, there are situations where we would like to know how much time and resources an algorithm might take when implemented. To measure performance of algorithms, we typic 13 min read Types of Asymptotic Notations in Complexity Analysis of AlgorithmsWe have discussed Asymptotic Analysis, and Worst, Average, and Best Cases of Algorithms. The main idea of asymptotic analysis is to have a measure of the efficiency of algorithms that don't depend on machine-specific constants and don't require algorithms to be implemented and time taken by programs 8 min read Data StructuresGetting Started with Array Data StructureArray is a collection of items of the same variable type that are stored at contiguous memory locations. It is one of the most popular and simple data structures used in programming. Basic terminologies of ArrayArray Index: In an array, elements are identified by their indexes. Array index starts fr 14 min read String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut 2 min read Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The 2 min read Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List: 2 min read Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first 2 min read Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems 2 min read Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most 4 min read Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of 3 min read Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this 15+ min read AlgorithmsSearching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input 2 min read Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ 3 min read Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution 14 min read Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get 3 min read Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net 3 min read Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of 3 min read Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. 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From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br 2 min read Interview PreparationInterview Corner: All Resources To Crack Any Tech InterviewThis article serves as your one-stop guide to interview preparation, designed to help you succeed across different experience levels and company expectations. Here is what you should expect in a Tech Interview, please remember the following points:Tech Interview Preparation does not have any fixed s 3 min read GfG160 - 160 Days of Problem SolvingAre you preparing for technical interviews and would like to be well-structured to improve your problem-solving skills? Well, we have good news for you! GeeksforGeeks proudly presents GfG160, a 160-day coding challenge starting on 15th November 2024. 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