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