## What is adjacency matrix and list explain with example?

The adjacency matrix, sometimes also called the connection matrix, of a simple labeled graph is a matrix with rows and columns labeled by graph vertices, with a 1 or 0 in position according to whether and. are adjacent or not. For a simple graph with no self-loops, the adjacency matrix must have 0s on the diagonal.

**What is adjacency matrix give example in data structure?**

An adjacency matrix is a matrix that contains rows and columns used to represent a simple labeled graph with the numbers 0 and 1 in the position of (VI, Vj), according to the condition of whether or not the two Vi and Vj are adjacent.

**What do you mean by adjacency list?**

In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. This is one of several commonly used representations of graphs for use in computer programs.

### What is adjacency matrix in discrete mathematics?

An adjacency matrix is a compact way to represent the structure of a finite graph. If a graph has n vertices, its adjacency matrix is an n × n n \times n n×n matrix, where each entry represents the number of edges from one vertex to another.

**Why adjacency matrix is suitable for dense graph?**

For a dense graph, O(e) = O(v2), and so adjacency matrices are a good representation strategy for dense graphs, because in big-O terms they don’t take up more space than storing all the edges in a linked list, and operations are much faster. If a graph is not dense, then we say the graph is sparse.

**When should we use adjacency matrix and when should we use adjacency lists some examples are helpful?**

It is recommended that we should use Adjacency Matrix for representing Dense Graphs and Adjacency List for representing Sparse Graphs. Note: Dense Graph are those which has large number of edges and sparse graphs are those which has small number of edges.

#### What is adjacency list data structure?

In graph theory and computer science, an adjacency list is a collection of unordered lists used to represent a finite graph. Each unordered list within an adjacency list describes the set of neighbors of a particular vertex in the graph.

**What is adjacency matrix in architecture?**

In interior design an adjacency matrix is a table that shows what spaces should and should not be near to each other on plan. Spending the time to draw this matrix means that you no longer have to leaf through your program every time you can’t remember if the client wants the Board Room close to the Break Room.