In a graph with a large number of vertices but relatively few edges (sparse graph), which representation would be most space-efficient?
Incidence Matrix
Adjacency Matrix
Edge List
None of the above
In a GPS navigation system, what graph algorithm is commonly used to find the shortest route between two locations represented as nodes on a road network?
Topological Sort
Dijkstra's Algorithm
Floyd-Warshall Algorithm
A* Search Algorithm
What is the purpose of topological sorting in directed acyclic graphs (DAGs)?
Finding the shortest path between any two vertices.
Calculating the minimum spanning tree of the graph.
Determining if the graph has a Hamiltonian cycle.
Finding a linear ordering of vertices where for every edge (u, v), u comes before v.
You are designing a social network and want to recommend friends to users. What graph algorithm would be most suitable for identifying potential friends based on shared connections?
Breadth-First Search (BFS)
Depth-First Search (DFS)
Bellman-Ford Algorithm
In the context of Kruskal's algorithm, what data structure is commonly used to efficiently detect cycles during edge addition?
Heap
Disjoint Union Set (Union-Find)
Stack
Queue
Kruskal's algorithm sorts edges in ascending order of their weights. What data structure is typically used for this sorting step?
Linked List
Social media platforms utilize graph analysis to detect communities or clusters of users with shared interests. What graph concept is employed to identify these densely connected groups?
Shortest Path
Minimum Spanning Tree
Graph Coloring
Community Detection
Which of the following situations would make Bellman-Ford algorithm a better choice than Dijkstra's algorithm?
Finding the shortest path in an unweighted graph
Finding the shortest path in a graph with negative edge weights
Finding the shortest path in a tree
Finding the shortest path in a dense graph
Consider a social network graph where vertices are users and edges are friendships. Which representation would be best for quickly finding all the friends of a particular user?
Adjacency List
Which representation would be most suitable for a graph where you primarily need to iterate over all edges efficiently?