What is the purpose of a weighted adjacency list in graph representation?

A weighted adjacency list is specifically designed to manage edges in a graph that have associated weights. In the context of graph representations, each vertex in the list is connected to its adjacent vertices along with weights that signify the cost, distance, or any quantitative value related to the edge connecting them. This structure is particularly useful in various applications such as shortest path algorithms, network flows, and other scenarios where the cost associated with traversing from one vertex to another is significant.

The weighted adjacency list allows for efficient storage and retrieval of this information compared to other representations, particularly for sparse graphs. Each entry in the list includes both the neighboring vertex and the weight, thus providing a clear and efficient way to access all necessary details for graph algorithms that require consideration of edge weights.