# when to use adjacency matrix vs list

Up to v2 edges if fully connected. • Dense graph: lots of edges. Up to O(v2) edges if fully connected. Adjacency Matrix vs. This is usually a space vs. time tradeoff. In a weighted graph, the edges This space-efficient way leads to slow searching (O(n)). Adjacency List vs Adjacency Matrix. 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. Fig 4. The adjacency matrix is a good way to represent a weighted graph. • The adjacency matrix is a good way to represent a weighted graph. So what we can do is just store the edges from a given vertex as an array or list. • Sparse graph: very few edges. Update matrix entry to contain the weight. Implementation of DFS using adjacency matrix Depth First Search (DFS) has been discussed before as well which uses adjacency list for the graph representation. raise the matrix to the 2nd power, or square it). Usually easier to implement and perform lookup than an adjacency list. The adjacency matrix is exactly what its name suggests -- it tells us which actors are adjacent, or have a direct path from one to the other. The Right Representation: List vs. Matrix There are two classic programmatic representations of a graph: adjacency lists and adjacency matrices. • The matrix always uses Θ(v2) memory. Instead of a list of lists, it is a 2D matrix that maps the connections to nodes as seen in figure 4. 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 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. In an adjacency list, each vertex is followed by a list, which contains only the n adjacent vertices. To construct the incidence matrix we need to mark the vertices and edges, that is, \$(x_1, x_1,\ldots, x_n)\$ and \$(u_1, u_2,\ldots, u_m)\$ respectively. Dense graph: lots of edges. 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. Each Node in this Linked list represents the reference to the other vertices which share an edge with the current vertex. The weights can also be stored in the Linked List Node. Every Vertex has a Linked List. Adjacency Matrix: Use this when you need to access the edge [math]a[i][j] [/math]as an [math]O(1)[/math] lookup often. We will treat "self-ties" as … adjacency matrix vs list, In an adjacency matrix, each vertex is followed by an array of V elements. Now suppose that we multiply this adjacency matrix times itself (i.e. In a weighted graph, the edges have weights associated with them. An example of an adjacency matrix. Sparse graph: very few edges. In the case of the adjacency matrix, we store 1 when there is an edge between two vertices else we store infinity. The adjacency matrix of an empty graph may be a zero matrix. This O(V)-space cost leads to fast (O(1)-time) searching of edges. List? Now in this section, the adjacency matrix will be used to represent the graph. an adjacency list. If you notice, we are storing those infinity values unnecessarily, as they have no use for us. In a sparse graph most entries will be 0 and waste a bunch of space. What I meant was that the vertex marking considered for the construction of the matrices is the same. Weights could indicate distance, cost, etc. An Adjacency matrix is just another way of representing a graph when using a graph algorithm. This section, the adjacency matrix of an empty graph may be a zero matrix,. Do is just store the edges from a given vertex as an array of V elements a matrix. By a list of lists, it is a good way to represent a weighted.. 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