10 Must Know Graph Algorithms

Story is covering all graph algorithms that are required while working with graphs.

Graph algorithms are computational procedures designed to analyze and manipulate graph structures, facilitating tasks such as pathfinding, connectivity analysis, and optimization in various applications like network routing and social network analysis.

1. Breadth-first search: Traverses a graph level by level, exploring all neighbors of a node before moving on to the next level.

2. Depth-first search: Explores as far as possible along each branch before backtracking, often implemented using recursion.

3. Shortest path: Finds the most efficient path between two nodes in terms of the sum of edge weights.

4. Cycle detection: Identifies the presence of cycles (loops) in a graph, crucial for detecting dependencies and avoiding infinite loops.

5. Minimum spanning tree: Finds the subset of edges that connects all vertices with the minimum total edge weight, forming a tree.

6. Strongly connected components: Divides a directed graph into strongly connected subgraphs, where each vertex is reachable from every other vertex.

7. Topological sorting: Orders the vertices of a directed acyclic graph in such a way that for every directed edge, the destination vertex comes after the source vertex.

8. Graph Colouring: Assigns colors to vertices of a graph such that no two adjacent vertices share the same color, often used in scheduling and resource allocation.

9. Maximum flow: Determines the maximum amount of flow that can be sent from a designated source to a designated sink in a flow network.

10. Matching: Identifies edges in a graph such that no two edges share a common vertex, often used in bipartite graph matching or assignment problems.