What does an adjacency matrix represent?

An adjacency matrix is a mathematical representation of a graph using a two-dimensional array, where both dimensions correspond to the vertices of the graph. Each cell in this matrix indicates whether there is an edge between a pair of vertices. If there is a connection (or edge) between vertices, the corresponding cell will typically contain a non-zero value (often 1, or the weight of the edge, if the graph is weighted); if there is no edge, the cell will usually contain a value of zero. This representation allows for quick lookup of connections between nodes in the graph, making it a foundational concept in graph theory.

The other options do not accurately describe the purpose or functionality of an adjacency matrix. The first option relates to tree data structures, which manage hierarchical data, while the third option refers to priority queues, which are used in algorithms that require sorting or managing prioritized tasks. The fourth option discusses graph traversal methods, such as depth-first or breadth-first search, which are separate concepts that although may utilize an adjacency matrix for their implementation, do not describe the matrix itself.