List? In the case of the adjacency matrix, we store 1 when there is an edge between two vertices else we store infinity. For use as a data structure, the main alternative to the adjacency list is the adjacency matrix. • The matrix always uses Θ(v2) memory. Adjacency Matrix A graph G = (V, E) where v= {0, 1, 2, . 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. An example of an adjacency matrix. It costs us space.. To fill every value of the matrix we need to check if there is an edge between every pair of vertices. So what we can do is just store the edges from a given vertex as an array or list. One is space requirement, and the other is access time. Assuming the graph has vertices, the time complexity to build such a matrix is .The space complexity is also . Please briefly Justify your choice. Fig 4. 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. An Adjacency matrix is just another way of representing a graph when using a graph algorithm. In a weighted graph, the edges . Each Node in this Linked list represents the reference to the other vertices which share an edge with the current vertex. Would you use the adjacency matrix structure or the adjacency list structure in each of the following cases? . If you notice, we are storing those infinity values unnecessarily, as they have no use for us. Instead of a list of lists, it is a 2D matrix that maps the connections to nodes as seen in figure 4. 2. The Right Representation: List vs. Matrix There are two classic programmatic representations of a graph: adjacency lists and adjacency matrices. Adjacency List: Adjacency List is the Array[] of Linked List, where array size is same as number of Vertices in the graph. Adjacency Lists. n-1} can be represented using two dimensional integer array of size n x n. int adj[20][20] can be used to store a graph with 20 vertices adj[i][j] = 1, indicates presence of edge between two vertices i and j.… Read More » The weights can also be stored in the Linked List Node. Fig 3: Adjacency Matrix . 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. Adjacency lists are the right data structure for most applications of graphs. Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. Every Vertex has a Linked List. The graph has 10,000 vertices and 20,000 edges, and it is important to use as little space as possible. Up to O(v2) edges if fully connected. The amount of such pairs of given vertices is . Adjacency List vs Adjacency Matrix. Adjacency Matrix vs. • The adjacency matrix is a good way to represent a weighted graph. • Sparse graph: very few edges. 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. 1. • Dense graph: lots of edges. There are 2 big differences between adjacency list and matrix. Data structures. Adjacency lists, in … Usually easier to implement and perform lookup than an adjacency list.

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