1. Dijkstra’s method: A basic method for determining the shortest route between graph nodes, such as road networks.
  2. Bellman-Ford method: Like Dijkstra’s, this method detects negative cycles in networks with negative edge weights.
  3. Floyd-Warshall Algorithm: Finds shortest routes in a weighted network with positive or negative edge weights but no negative cycles.
  4. Breadth-First Search (BFS): A layer-wise graph traversal technique from a specified node.
  5. Depth-First Search (DFS): This method traverses over a graph, utilizing a stack to remember the next vertex.
  6. Kruskal’s method: A greedy method that finds a minimal spanning tree for a linked weighted network to minimize its weight.
  7. Prim’s technique: Another greedy technique for weighted undirected graph minimum spanning trees.
  8. Topological Sorting: Orders directed acyclic graph (DAG) vertices linearly, preserving dependencies.
  9. Tarjan’s Algorithm: Used to locate highly linked components in a directed graph, which helps explain its structure.
  10. Kosaraju’s Algorithm: Like Tarjan’s, it detects highly linked components in directed graphs.
  11. In sparse directed weighted graphs, Johnson’s Algorithm discovers shortest routes between all pairs of vertices.
  12. A search algorithm: A popular pathfinding and graph traversal technique, this one efficiently reaches the objective.
  13. Ford-Fulkerson The maximum flow in a flow network is calculated using an algorithm.
  14. The Ford-Fulkerson technique for determining network maximum flow is implemented by the Edmonds-Karp algorithm.
  15. Hopcroft-Karp Algorithm: Finds bipartite graph maximum cardinality matching.
  16. Borůvka’s method: Aged method for graph minimal spanning tree, notable for its simplicity.
  17. Fleury’s Algorithm: An elegant graph Eulerian route and circuit design approach.
  18. Christofides Algorithm: Polynomial-time heuristic for the traveling salesman problem.
  19. Bron-Kerbosch Algorithm: Lists all maximum cliques in an undirected graph.
  20. Girvan-Newman By gradually eliminating edges from the original network, this method finds communities.

Each of these algorithms plays a vital role in computer science and applied mathematics, helping to solve complex problems in network analysis, computer graphics, and optimization problems. They represent a broad spectrum of approaches, from greedy algorithms to more complex heuristic and recursive strategies. Their applications range from simple pathfinding in video games to complex network analysis in computational biology and social network analysis.

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Graph Theory