Graph Algorithms Comparison

Big Table

Algorithm	Purpose	Main Data Structure	Time
BFS	Visit level by level	Queue	O(V + E)
DFS	Visit deep first	Stack / Recursion	O(V + E)
Dijkstra	Shortest path with non-negative weights	Priority Queue	O((V + E) log V)
Topological Sort	Order tasks in DAG	Queue / Indegree	O(V + E)

Easy Comparison

BFS

• best for nearest nodes in unweighted graphs
• explores by layers

DFS

• best for deep exploration
• useful for recursion-style graph problems

Dijkstra

• best for weighted shortest path
• slower than BFS because of priority queue work

Topological Sort

• not a path algorithm
• best for dependency ordering

When To Use

Choose BFS if:

• graph is unweighted
• shortest number of edges matters

Choose DFS if:

• you need traversal, cycle checks, or components

Choose Dijkstra if:

• edges have non-negative weights
• shortest weighted path is needed

Choose Topological Sort if:

• tasks have dependencies
• graph is a DAG