Which algorithm is more suitable for finding the shortest path in a graph with negative edge weights?
Bellman-Ford algorithm
Kruskal's algorithm
Prim's algorithm
Dijkstra's algorithm
Which of the following operations is typically less efficient with an edge list representation compared to an adjacency matrix?
Adding a new edge
Checking if the graph is connected
Determining the degree of a vertex
Finding all edges connected to a specific vertex
Which graph traversal algorithm is most efficient for detecting cycles in a directed graph, crucial for identifying dependencies in a project management system?
Kruskal's Algorithm
Depth-First Search (DFS)
Breadth-First Search (BFS)
Prim's Algorithm
Which algorithm efficiently calculates the shortest paths between all pairs of nodes in a weighted graph, useful for analyzing network connectivity in social networks?
Bellman-Ford Algorithm
Floyd-Warshall Algorithm
Dijkstra's Algorithm
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?
Community Detection
Graph Coloring
Shortest Path
Minimum Spanning Tree
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?
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
A* Search Algorithm
An incidence matrix for a graph with 'V' vertices and 'E' edges will have dimensions:
E x E
Depends on the graph's connectivity
V x E
V x V
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 shortest geographical distance.
Finding the path with the fewest road closures.
Finding the path with the least overall travel time, considering delays.
Finding the path with the lowest fuel consumption.
Which of the following real-world scenarios is best modeled using a weighted graph with potentially negative edge weights?
Representing relationships in a family tree
Finding the shortest route between two cities on a map
Modeling financial transactions where profits and losses are possible
Tracking the spread of information in a social network