Skill

role-algorithms:graph-algorithms

Implements graph algorithms — BFS/DFS traversal, shortest paths (Dijkstra, Bellman-Ford, Floyd-Warshall, A*, Johnson's), minimum spanning trees (Kruskal, Prim), topological sort, strongly connected components (Tarjan, Kosaraju), maximum flow (Ford-Fulkerson, Dinic), and bipartite matching (Hopcroft-Karp, Hungarian). Use when solving traversal, shortest path, network flow, connectivity, or scheduling problems.

Install

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

Tool Access

This skill is limited to using the following tools:

ReadGrepGlobBash

Preview

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

Supporting Assets

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

SKILL.md

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Stats

Parent Repo Stars9

Parent Repo Forks0

Last CommitMar 3, 2026

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role-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