Adjacency Matrix vs. Up to O(v2) edges if fully connected. One is space requirement, and the other is access time. Usually easier to implement and perform lookup than an adjacency list. On the other hand, the adjacency matrix allows testing whether two vertices are adjacent to each other in constant time; the adjacency list is slower to support this operation. Fig 4. If you notice, we are storing those infinity values unnecessarily, as they have no use for us. 2. In a weighted graph, the edges Assuming the graph has vertices, the time complexity to build such a matrix is .The space complexity is also . • The adjacency matrix is a good way to represent a weighted graph. • Sparse graph: very few edges. Depending upon the application, we use either adjacency list or adjacency matrix but most of the time people prefer using adjacency list over adjacency matrix. The adjacency matrix, also called the connection matrix, is a matrix containing rows and columns which is used to represent a simple labelled graph, with 0 or 1 in the position of (V i , V j) according to the condition whether V i and V j are adjacent or not. The amount of such pairs of given vertices is . Every Vertex has a Linked List. . Please briefly Justify your choice. List? • Dense graph: lots of edges. So what we can do is just store the edges from a given vertex as an array or list. Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. Adjacency lists, in … The weights can also be stored in the Linked List Node. Adjacency lists are the right data structure for most applications of graphs. An Adjacency matrix is just another way of representing a graph when using a graph algorithm. Would you use the adjacency matrix structure or the adjacency list structure in each of the following cases? For use as a data structure, the main alternative to the adjacency list is the adjacency matrix. The graph has 10,000 vertices and 20,000 edges, and it is important to use as little space as possible. Adjacency Lists. The Right Representation: List vs. Matrix There are two classic programmatic representations of a graph: adjacency lists and adjacency matrices. Adjacency List vs Adjacency Matrix. Fig 3: Adjacency Matrix . Adjacency List: Adjacency List is the Array[] of Linked List, where array size is same as number of Vertices in the graph. In the adjacency matrix of an undirected graph, the value is considered to be 1 if there is an edge between two vertices, else it is 0. • The matrix always uses Θ(v2) memory. . An example of an adjacency matrix. 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