Description: The edge list is a graph representation consisting of a collection of edges, where each edge is defined as a pair of vertices. This structure is particularly useful for compactly representing graphs, as it only stores the connections between nodes without needing to include additional information about the graph’s structure. In an edge list, each element of the list represents a direct connection between two vertices, allowing for easy identification of relationships between them. This representation is especially space-efficient when the graph is sparse, meaning the number of edges is much lower than the square of the number of vertices. Additionally, the edge list facilitates certain operations, such as iterating over the edges of the graph, which can be advantageous in algorithms that require exploring connections between nodes. However, its use may be less efficient in dense graphs, where other representations, such as the adjacency matrix, might be more suitable. In summary, the edge list is a fundamental way to represent graphs, standing out for its simplicity and efficiency in representing relationships between nodes.
Uses: The edge list is used in various applications within graph theory and computer science. It is common in graph search and traversal algorithms, such as those for finding the shortest path. It is also employed in the representation of social networks, where users are the vertices and the connections between them are the edges. Additionally, it is used in modeling transportation systems, where locations are the vertices and the routes between them are the edges.
Examples: A practical example of an edge list is the representation of a graph describing a road network. If we consider three cities A, B, and C, and the roads connecting them, the edge list could be: [(A, B), (B, C), (A, C)]. This indicates that there is a road between A and B, another between B and C, and one more between A and C.
