Dijkstra Algorithm Simulator

Single-source shortest paths

Dijkstra's algorithm finds shortest paths from one source vertex in a graph with non-negative edge weights. This simulator uses an undirected weighted graph and a min-priority queue.

Binary-heap implementationO((V + E) log V)

Edge requirementNon-negative

OutputDistance + path

Graph typeUndirected

Graph editing and algorithm controls

New vertex label

Edge endpoint 1

Edge endpoint 2

Weight

Source

Target

Animation speed400 ms

Example weighted graph loaded. Drag vertices or run Dijkstra.

Vertices0

Edges0

Settled vertices0

Relaxations0

Current step

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Selected shortest path

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Min-priority queue

Distance and predecessor table

Vertex	Distance	Previous	State

Relaxation rulecandidate =
    distance[current] + edgeWeight

if candidate < distance[neighbor]:
    distance[neighbor] = candidate
    previous[neighbor] = current
    push updated entry
    into the min-priority queue

Stale queue entries are ignored.

Dijkstra concepts

Greedy settlement

The unvisited vertex with the smallest tentative distance becomes settled. With non-negative weights, its shortest distance can no longer improve.

Relaxation

Each outgoing edge tests whether reaching a neighbor through the current vertex gives a shorter route.

Path reconstruction

The predecessor table stores the previous vertex on each best-known route. Following those links backward reconstructs the shortest path.

Unreachable vertices

A vertex outside the source's connected component keeps distance infinity and has no shortest path from that source.

When Dijkstra applies

Condition	Result
All edge weights are non-negative	Dijkstra is correct.
A negative edge exists	Use Bellman–Ford or another suitable algorithm.
All weights are equal	BFS is sufficient.
Need all-pairs shortest paths	Run from each source or use an all-pairs algorithm.