Can two-dimensional arrays be used to represent graphs?

Yes, two-dimensional arrays can indeed be used to represent graphs in computer science.

In computer science, a graph is a data structure that consists of a set of nodes (or vertices) and a set of edges. Each edge connects a pair of vertices. Graphs can be used to represent many different types of data, such as social networks, web pages, biological networks, and more.

A two-dimensional array, also known as a matrix, can be used to represent a graph. This is often referred to as an adjacency matrix. In an adjacency matrix, the cell at the intersection of row i and column j represents the edge between vertices i and j. If there is an edge between these vertices, the cell contains a 1 (or sometimes the weight of the edge); if there is no edge, the cell contains a 0.

For example, consider a graph with three vertices (A, B, and C) and three edges (A-B, B-C, and A-C). The adjacency matrix for this graph would be a 3x3 matrix where the first row and first column represent vertex A, the second row and column represent vertex B, and the third row and column represent vertex C. The cell at the intersection of the first row and second column would contain a 1, indicating that there is an edge between vertices A and B.

This method of representing graphs is particularly useful when the graph is dense, meaning it has a large number of edges. However, it can be inefficient for sparse graphs, as it requires space for every possible edge, even if it does not exist.

In addition to adjacency matrices, graphs can also be represented using other data structures, such as adjacency lists, incidence matrices, and edge lists. The choice of representation depends on the specific requirements of the problem at hand, including factors such as the size of the graph, the density of the graph, and the operations that need to be performed on the graph.