Dijkstra's algorithm's time complexity primarily depends on the data structure used to manage the "unvisited" nodes, most commonly a priority queue, and therefore different implementations can significantly impact its time complexity; with a basic array-based approach, the time complexity is O(V^2) (where V is the number of vertices), but using a priority queue, typically implemented with a heap, brings the complexity down to O(E log V) (where E is the number of edges) which is usually much more efficient for large graphs.