Skill

role-algorithms:graph-algorithms

Implements graph algorithms including BFS/DFS traversal, shortest paths (Dijkstra, Bellman-Ford, A*), MSTs (Kruskal, Prim), topological sort, SCCs (Tarjan, Kosaraju), max flow (Dinic), bipartite matching. Use for pathfinding, network flow, connectivity, scheduling.

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npx claudepluginhub rnavarych/alpha-engineer --plugin role-algorithms

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- Modeling a problem as a graph and selecting the right traversal or optimization algorithm

Supporting Files

references/advanced-graph.mdreferences/representations-and-traversal.mdreferences/shortest-paths-and-mst.md

SKILL.md

29 lines · ~575 tokens

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Last CommitMar 3, 2026

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role-algorithms:graph-algorithms

Graph Algorithms

When to use

Modeling a problem as a graph and selecting the right traversal or optimization algorithm

Finding shortest paths with positive weights (Dijkstra), negative weights (Bellman-Ford), or all pairs (Floyd-Warshall)

Building minimum spanning trees for network design problems

Resolving task dependency order via topological sort

Finding strongly connected components for 2-SAT or condensation graphs

Computing max flow / min cut or bipartite matching for allocation problems

Pathfinding in grids or maps with a heuristic (A*)

Core principles

Representation determines complexity — adjacency list for sparse, matrix for dense; wrong choice costs orders of magnitude

Negative weights break Dijkstra — if any edge weight is negative, use Bellman-Ford; don't assume inputs are clean

Max-flow = min-cut — network flow problems often hide as cut problems; recognize the dual

Topological sort = DP on a DAG — if you can sort topologically, you can compute DP in one pass

Kruskal needs Union-Find; Prim needs a heap — pick based on graph density, not familiarity

Reference Files

references/representations-and-traversal.md — adjacency list/matrix/edge list selection criteria, BFS (unweighted shortest path, bipartite check), DFS (cycle detection, articulation points), DFS edge classification

references/shortest-paths-and-mst.md — Dijkstra, Bellman-Ford, Floyd-Warshall, A* (admissible heuristics), Johnson's algorithm, algorithm selection table, Kruskal and Prim with cut/cycle properties

references/advanced-graph.md — topological sort (Kahn's BFS + DFS post-order), SCCs (Tarjan and Kosaraju), Dinic's max flow, bipartite matching (Hopcroft-Karp, Hungarian, Kuhn's), flow application patterns

Graph Algorithms

When to use

Modeling a problem as a graph and selecting the right traversal or optimization algorithm
Finding shortest paths with positive weights (Dijkstra), negative weights (Bellman-Ford), or all pairs (Floyd-Warshall)
Building minimum spanning trees for network design problems
Resolving task dependency order via topological sort
Finding strongly connected components for 2-SAT or condensation graphs
Computing max flow / min cut or bipartite matching for allocation problems
Pathfinding in grids or maps with a heuristic (A*)

Core principles

Representation determines complexity — adjacency list for sparse, matrix for dense; wrong choice costs orders of magnitude
Negative weights break Dijkstra — if any edge weight is negative, use Bellman-Ford; don't assume inputs are clean
Max-flow = min-cut — network flow problems often hide as cut problems; recognize the dual
Topological sort = DP on a DAG — if you can sort topologically, you can compute DP in one pass
Kruskal needs Union-Find; Prim needs a heap — pick based on graph density, not familiarity

Reference Files

references/representations-and-traversal.md — adjacency list/matrix/edge list selection criteria, BFS (unweighted shortest path, bipartite check), DFS (cycle detection, articulation points), DFS edge classification
references/shortest-paths-and-mst.md — Dijkstra, Bellman-Ford, Floyd-Warshall, A* (admissible heuristics), Johnson's algorithm, algorithm selection table, Kruskal and Prim with cut/cycle properties
references/advanced-graph.md — topological sort (Kahn's BFS + DFS post-order), SCCs (Tarjan and Kosaraju), Dinic's max flow, bipartite matching (Hopcroft-Karp, Hungarian, Kuhn's), flow application patterns

role-algorithms:graph-algorithms

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role-algorithms:graph-algorithms

Popularity

Invocation

Tool Access

Context Preview

Supporting Files

SKILL.md

Graph Algorithms

When to use

Core principles

Reference Files

Similar Skills

Help us improve

Graph Algorithms

When to use

Core principles

Reference Files