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
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 of the following operations is typically less efficient with an edge list representation compared to an adjacency matrix?
Adding a new edge
Finding all edges connected to a specific vertex
Checking if the graph is connected
Determining the degree of a vertex
Which of the following algorithms can handle negative weights in a weighted graph without issues?
Prim's Algorithm
Dijkstra's Algorithm
Breadth-First Search (BFS)
Bellman-Ford Algorithm
Which graph traversal algorithm is most efficient for detecting cycles in a directed graph, crucial for identifying dependencies in a project management system?
Depth-First Search (DFS)
Kruskal's Algorithm
How does the concept of 'distance' in a weighted graph differ from that in an unweighted graph?
There is no difference; 'distance' has the same meaning in both types of graphs.
Distance is only defined for unweighted 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.
In weighted graphs, 'distance' always refers to geographical distance, while in unweighted graphs, it can represent abstract relationships.
Which representation would be most suitable for a graph where you primarily need to iterate over all edges efficiently?
In an undirected graph represented using an incidence matrix, what would be the sum of the values in a single column?
1
2
V (number of vertices)
0
Topological sorting is possible for which type of graph?
Undirected graphs
Weighted graphs
Complete graphs
Directed acyclic graphs (DAGs)
Why are negative weights problematic for some shortest path algorithms?
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.
Negative weights can lead to cycles where the total weight decreases with each iteration, confusing the algorithm.
All of the above