Description: Density in graph theory is a measure that quantifies how many edges (or connections) exist in a graph compared to the maximum possible number of edges it could have. It is mathematically defined as the ratio of the number of edges present in the graph to the maximum number of edges it could have, which is calculated as n(n-1)/2 for an undirected graph, where n is the number of vertices. This metric provides a clear insight into how ‘complete’ or ‘connected’ a graph is. A dense graph has a density close to 1, indicating that most of the possible edges are present, while a sparse graph has a density close to 0, suggesting that there are few edges compared to the total possible. Density is useful for classifying graphs and understanding their structure, as it influences the behavior of algorithms that operate on them, such as search and traversal algorithms. Additionally, density can affect the computational complexity of certain problems in graph theory, making some algorithms more efficient on dense graphs than on sparse ones.
