How does the concept of 'distance' in a weighted graph differ from that in an unweighted graph?
In weighted graphs, 'distance' always refers to geographical distance, while in unweighted graphs, it can represent abstract relationships.
There is no difference; 'distance' has the same meaning in both types of graphs.
In a weighted graph, 'distance' represents the sum of edge weights along a path, while in an unweighted graph, it's the number of edges.
Distance is only defined for unweighted graphs.
Which algorithm efficiently calculates the shortest paths between all pairs of nodes in a weighted graph, useful for analyzing network connectivity in social networks?
Floyd-Warshall Algorithm
Dijkstra's Algorithm
Bellman-Ford Algorithm
Kruskal's Algorithm
Which of the following algorithms can handle negative weights in a weighted graph without issues?
Prim's Algorithm
Breadth-First Search (BFS)
In a weighted graph representing a road network with construction delays (represented by negative weights), what does finding the 'shortest path' mean?
Finding the path with the least overall travel time, considering delays.
Finding the path with the shortest geographical distance.
Finding the path with the fewest road closures.
Finding the path with the lowest fuel consumption.
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?
Minimum Spanning Tree
Graph Coloring
Community Detection
Shortest Path
Which of the following algorithms is typically used for topological sorting?
Prim's algorithm
Kruskal's algorithm
Depth-First Search (DFS)
Dijkstra's algorithm
In the context of Kruskal's algorithm, what data structure is commonly used to efficiently detect cycles during edge addition?
Heap
Stack
Queue
Disjoint Union Set (Union-Find)
Why are negative weights problematic for some shortest path algorithms?
Negative weights can lead to cycles where the total weight decreases with each iteration, confusing the algorithm.
These algorithms assume that adding an edge to a path always increases its total weight.
Algorithms like Dijkstra's rely on the principle that shorter paths are always discovered before longer ones.
All of the above
If you need to perform frequent edge insertions and deletions in a graph, which representation might be preferred?
Incidence Matrix
Adjacency Matrix
Edge List
It depends on the specific graph operations
You are tasked with designing a system to schedule tasks with dependencies between them. What graph data structure would be most appropriate to represent these dependencies?
Directed Acyclic Graph (DAG)
Undirected Graph
Complete Graph
Bipartite Graph