Description: An adjacency matrix is a mathematical representation of a finite graph, organized in the form of a square matrix. In this matrix, the rows and columns correspond to the vertices of the graph, and the elements of the matrix indicate whether there is a connection (or edge) between pairs of vertices. If there is an edge between vertex i and vertex j, the element at position (i, j) in the matrix takes a specific value (usually 1 or the weight of the edge), while if there is no connection, the value is 0. This representation is particularly useful for dense graphs, where most pairs of vertices are connected. The adjacency matrix allows for operations such as path searching, cycle detection, and connectivity analysis to be performed efficiently. Additionally, its structure facilitates implementation in graph theory algorithms, such as Dijkstra’s algorithm for finding the shortest path. However, its use may be less efficient in sparse graphs, where most elements of the matrix are zeros, as it consumes more memory space. In summary, the adjacency matrix is a fundamental tool in the representation and analysis of graphs, providing a clear and structured way to visualize the relationships between vertices.
