role-algorithms:graph-algorithms

To find the shortest path with negative edge weights, you can use the Bellman-Ford or Johnson's algorithms. Both handle negative weights, and Johnson's algorithm is particularly effective for computing all-pairs shortest paths in sparse graphs containing negative weight edges.

The best way to find strongly connected components (SCCs) is by using Tarjan's or Kosaraju's algorithms. Both traverse the directed graph to identify maximal subgraphs where every node is reachable from every other node, which is essential for dependency analysis.

You solve maximum flow problems using Ford-Fulkerson or Dinic's algorithms, and handle bipartite matching with Hopcroft-Karp or the Hungarian algorithm. These optimize resource allocation and flow capacities across interconnected network structures.

Yes, you can use topological sort for task scheduling and dependency resolution. It linearly orders the vertices of a directed acyclic graph so that for every directed edge from node A to node B, node A comes before node B in the ordering.

Use Dijkstra for finding the shortest paths from a single source to all other nodes with positive weights. Use A* when you have a specific target node and a heuristic function, making it more efficient for targeted pathfinding and traversal.

You can find a minimum spanning tree using Kruskal's or Prim's algorithms. Both optimize network connectivity by selecting a subset of edges that connects all vertices together without any cycles and with the minimum possible total edge weight.