In the case of the adjacency matrix, we store 1 when there is an edge between two vertices else we store infinity. Up to O(v2) edges if fully connected. Each edge in the network is indicated by listing the pair of nodes that are connected. Adjacency List vs Adjacency Matrix. n = number of vertices m = number of edges m u = number of edges leaving u yAdjacency Matrix Uses space O(n2) Can iterate over all edges in time O(n2) Can answer “Is there an edge from u to v?” in O(1) time Better for dense (i.e., lots of edges) graphs yAdjacency List Uses space O(m+n) Such places include Cormen et al. • The adjacency matrix is a good way to represent a weighted graph. 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. • The matrix always uses Θ(v2) memory. In adjacency matrix representation, memory used to represent graph is O(v 2). or Wikipedia. Usually easier to implement and perform lookup than an adjacency list. So transpose of the adjacency matrix is the same as the original. For example, the adjacency list for the Apollo 13 network is as follows: Tom Hanks, Bill Paxton. If the graph is undirected then when there is an edge between (u,v), there is also an edge between (v,u). First of all you've understand that we use mostly adjacency list for simple algorithms, but remember adjacency matrix is also equally (or more) important. Instead of a list of lists, it is a 2D matrix that maps the connections to nodes as seen in figure 4. An adjacency list, also called an edge list, is one of the most basic and frequently used representations of a network. Fig 4. Tom Hanks, Kevin Bacon • Sparse graph: very few edges. In a weighted graph, the edges However, using a sparse matrix representation like with Compressed Row Storage representation, the memory requirement is just in O(number of non-zeros) = O(number of edges), which is the same as using lists. Fig 3: Adjacency Matrix . 's book, or StackOverFlow : Size of a graph using adjacency list versus adjacency matrix? List? For use as a data structure, the main alternative to the adjacency list is the adjacency matrix. • Dense graph: lots of edges. If you notice, we are storing those infinity values unnecessarily, as they have no use for us. . So we can save half the space when representing an undirected graph using adjacency matrix. Tom Hanks, Gary Sinise. An Adjacency matrix is just another way of representing a graph when using a graph algorithm. So what we can do is just store the edges from a given vertex as an array or list. The Right Representation: List vs. Matrix There are two classic programmatic representations of a graph: adjacency lists and adjacency matrices. The adjacency matrix, on the other hand, does it in the following matrix format: 01111 10010 10011 11101 10110 It shows that if the 1st node and 2nd node are connected, there is a 1 at the grid[1][2] position, and 0 if the 2 nodes aren't connected, or if they are the same nodes. Adjacency Matrix Definition. 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 » . Adjacency Matrix vs. Adjacency Matrix or Adjacency List? An example of an adjacency matrix. 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