In which of the following cases adjacency list should be preferred over adjacency matrix for storing graph?

In which of the following cases adjacency list should be preferred over adjacency matrix for storing graph?

We prefer adjacency list. But if the graph is dense then the number of edges is close to (the complete) n(n−1)/2, or to n2 if the graph is directed with self-loops.

How do you store an efficient graph?

There are three ways to store a graph in memory:

1. Nodes as objects and edges as pointers.
2. A matrix containing all edge weights between numbered node x and node y.
3. A list of edges between numbered nodes.

What are the advantages and drawbacks of adjacency matrix?

Advantages and Disadvantages Adjacency matrices are helpful when we need to quickly check if two nodes have a direct edge or not. However, the main disadvantage is its large memory complexity. The adjacency matrix is most helpful in cases where the graph doesn’t contain a large number of nodes.

Where should graph data be stored?

Graph data is kept in store files, each of which contain data for a specific part of the graph, such as nodes, relationships, labels and properties. Dividing the storage in this way facilitates highly performant graph traversals (as detailed above).

What is the difference between a sparse and a dense graph?

There is no strict distinction between sparse and dense graphs. Typically, a sparse (connected) graph has about as many edges as vertices, and a dense graph has nearly the maximum number of edges.

How is an adjacency matrix similar to an array?

Adjacency Matrix: Adjacency Matrix is a 2D array of size V x V where V is the number of vertices in a graph. Let the 2D array be adj [] [], a slot adj [i] [j] = 1 indicates that there is an edge from vertex i to vertex j.

What is a nonzero value in the adjacency matrix?

If the adjacency matrix is multiplied by itself (matrix multiplication), if there is a nonzero value present in the ith row and jth column, there is a route from V to V j of length equal to two. It does not specify the path though there is a path created. The nonzero value indicates the number of distinct paths present.

How is the vertex matrix related to the adjacency matrix?

The vertex matrix is an array of numbers which is used to represent the information about the graph. Some of the properties of the graph correspond to the properties of the adjacency matrix, and vice versa.

How is an adjacency matrix used in an undirected graph?

Adjacency matrix for undirected graph is always symmetric. Adjacency Matrix is also used to represent weighted graphs. If adj [i] [j] = w, then there is an edge from vertex i to vertex j with weight w. Let us consider a graph to understand the adjacency list and adjacency matrix representation. Let the undirected graph be: