Part 1a: Generate a random 4 by 4 matrix using https://onlinemathtools.com/generate-random-matrix. Let that matrix represent the adjacency matrix for a graph with 4 nodes V={A,K,C,D} Draw the graph. Part 1b: Create the adj. List representation of the graph you generated in part 1a Part 2: Please run BFS on the graph above from node C. Please show the data structures used (i.e., lists queues ...)

When trying to represent a graph, why is it preferable to make use of an adjacency matrix as opposed to an adjacency list?

Given the graph class using the adjacency matrix representation, Implement the DFS algorithm on graph using the adjacency matrix representation. You have to use the graph code as a starting point, and add the DFS method in the graph class similar to the BFS method already present in the Graph class.   Should be coded in C++

Python Graph Algorithms: Minimum Spanning Trees Note: There are helper functions (see 'required' below), and some of them (like Kruskal's Algorithm, WeightedQuickUnion, and such) can help answering this problem. Problem: Suppose you are an engineer working on designing a road network for a new town. The town has many residential areas and commercial centers that need to be connected efficiently. You decided to represent the town as a connected, undirected graph where each vertex represents a location, and each edge represents a road connecting two locations. The weight of each edge represents the distance between the two locations. To ensure the road network is efficient, you need to find the minimum spanning tree of the graph. However, due to budget constraints, you can only construct roads with a maximum distance limit. You need to determine for how many pairs of locations, the minimum spanning tree of the graph remains the same when the maximum distance limit of a road is increased…