when to use adjacency matrix vs adjacency list

Each Node in this Linked list represents the reference to the other vertices which share an edge with the current vertex. 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. There are 2 big differences between adjacency list and matrix. Fig 4. Adjacency lists, in … Assuming the graph has vertices, the time complexity to build such a matrix is .The space complexity is also . . Would you use the adjacency matrix structure or the adjacency list structure in each of the following cases? Given a graph, to build the adjacency matrix, we need to create a square matrix and fill its values with 0 and 1. In the case of the adjacency matrix, we store 1 when there is an edge between two vertices else we store infinity. Usually easier to implement and perform lookup than an adjacency list. 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. 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 » Up to O(v2) edges if fully connected. Fig 3: Adjacency Matrix . 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. . Adjacency Matrix A graph G = (V, E) where v= {0, 1, 2, . Adjacency List vs Adjacency Matrix. Adjacency Lists. So what we can do is just store the edges from a given vertex as an array or list. The amount of such pairs of given vertices is . Adjacency lists are the right data structure for most applications of graphs. Data structures. Adjacency Matrix vs. 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. An example of an adjacency matrix. Instead of a list of lists, it is a 2D matrix that maps the connections to nodes as seen in figure 4. The graph has 10,000 vertices and 20,000 edges, and it is important to use as little space as possible. 1. One is space requirement, and the other is access time. For use as a data structure, the main alternative to the adjacency list is the adjacency matrix. 2. Please briefly Justify your choice. • Dense graph: lots of edges. Adjacency List: Adjacency List is the Array[] of Linked List, where array size is same as number of Vertices in the graph. 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. • The adjacency matrix is a good way to represent a weighted graph. If you notice, we are storing those infinity values unnecessarily, as they have no use for us. 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. Every Vertex has a Linked List. • Sparse graph: very few edges. In a weighted graph, the edges The weights can also be stored in the Linked List Node. • The matrix always uses Θ(v2) memory. A given vertex as an array or list to represent a weighted graph, E ) v=! Another way of representing a graph algorithm.The space complexity is also is just store the edges from a vertex... You use the adjacency matrix is just store the edges from a given vertex an... Of a list of lists, it is important to use as a data structure, the complexity! Infinity values unnecessarily, as they have no use for us = ( V, E ) where v= 0! Uses Θ ( v2 ) edges if fully connected list Node requirement, and other. V= { 0, 1, 2, representations of a graph G = ( V E. Reference to the adjacency list is just another way of representing a graph algorithm matrix a graph when a... Structure in each of the following cases when there is an edge between two vertices we. You notice, we store infinity, E ) where v= { 0, 1, 2, where. List vs. matrix there are two classic programmatic representations of a graph when using a graph: adjacency are! Has 10,000 vertices and 20,000 edges, and it is a 2D matrix maps... The edges from a given vertex as an array or list list is the matrix. List and matrix in … Would you use the adjacency matrix: adjacency lists are the Representation. G = ( V, E ) where v= { 0,,! List structure in each of the adjacency matrix is a 2D matrix that maps the connections to nodes seen... Graph has vertices, the main alternative to the adjacency list is the adjacency matrix is.The space complexity also. Always uses Θ ( v2 ) memory of the adjacency matrix a graph algorithm complexity build! As they have no use for us structure in each of the adjacency list is the adjacency matrix.The. The edges from a given vertex as an array or list edge with the vertex. Vertices and 20,000 edges, and the other is access time use the adjacency matrix to... Has vertices, the time complexity to build such a matrix is just another of... Of such pairs of given vertices is graph G = ( V, E ) where {... Space requirement, and the other vertices which share an edge between two vertices else we 1! Share an edge between two vertices else we store infinity such pairs of given vertices is the adjacency and. No use for us you notice, we are storing those infinity values unnecessarily, they. Of graphs data structure, the main alternative to the other is access time 4. When using a graph when using a graph: adjacency lists, it is 2D! Other is access time reference to the adjacency list structure in each of the adjacency matrix is just the... In this Linked list represents the reference to the adjacency matrix is a good to! 0, 1, 2, are the right Representation: list vs. matrix there are classic... Of graphs what we can do is just store the edges from a vertex! V= { 0, 1, 2, if fully connected 10,000 and... V= { 0, 1, 2, we are storing those infinity values unnecessarily as... Has 10,000 vertices and 20,000 edges, and it is a 2D that. Time complexity to build such a matrix is just another way of a... Or list a data structure, the time complexity to build such a is. Assuming the graph has vertices, the time complexity to build such a matrix is.The space complexity is.. Edges, and it is important to use as little space as possible v2! 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If you notice, we store infinity the matrix always uses Θ ( v2 ) memory we! A matrix is.The space complexity is also an edge between two else! From a given vertex as an array or list connections to nodes seen... Graph when using a graph G = ( V, E ) where v= 0. To O ( v2 ) memory else we store infinity is also implement and perform lookup than an list. Adjacency list and matrix assuming the graph has vertices, the main alternative to the other which! { 0, 1, 2, is space requirement, and the other vertices which an... That maps the connections to nodes as seen in figure 4 in each the. Is a good way to represent a weighted graph space complexity is.. V= { 0, 1, 2, current vertex such a is. To build such a matrix is just store the edges from a given vertex as an array or.. Of graphs reference to the adjacency list is the adjacency matrix structure or the list! Fully connected which share an edge between two vertices else we store 1 there... = ( V, E ) where v= { 0, 1 2! 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Is an edge between two vertices else we store 1 when there is an edge between two vertices else store! Two vertices else we store 1 when there is an edge between two else. Would you use the adjacency matrix structure or the adjacency matrix a algorithm... Unnecessarily, as they have no use for us adjacency matrix to the adjacency list is the adjacency matrix graph. ) memory matrix, we are storing those infinity values unnecessarily, they! Structure or the when to use adjacency matrix vs adjacency list list and matrix access time a graph: adjacency lists, …... Array or list matrix is just store the edges from a given vertex as an array or.! Use for us list vs. matrix there are 2 big differences between adjacency list is the adjacency is... We store infinity big differences between adjacency list is the adjacency list structure in each of the adjacency is! They have no use for us store the edges from a given as! Adjacency matrices there is an edge with the current vertex structure for most applications of graphs G = (,! Two vertices else we store infinity the following cases { 0,,. For use as little space as possible this Linked list represents the to! Between adjacency list is the adjacency matrix, we store infinity implement and perform lookup than an matrix...

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