When we talk about how to represent graphs, we often forget about the edge list. But this simple method has some great advantages that make it useful in certain situations.

First, an edge list is really easy to understand and work with. It shows a graph as a list of its edges, which are just connections made from two points called vertices. This is a lot simpler than other methods, like adjacency matrices, which can be more complicated. Because of its simplicity, an edge list is perfect for quick data entry and is clear to read, especially when working with graphs that don’t have many edges.

Also, edge lists use less memory compared to adjacency matrices, especially when the graph is sparse. A sparse graph is one that has many fewer edges than it could possibly have. In these cases, adjacency matrices use a lot of space, about $O(n^2)$, where $n$ is the number of vertices. On the other hand, edge lists only need $O(m)$ space, where $m$ is the number of edges. This makes edge lists much more efficient in terms of memory usage.

Beyond just using less memory, edge lists can make certain tasks easier and faster. For example, if you need to check if an edge exists or if you want to travel through the graph, doing this with an edge list can sometimes be quicker than with an adjacency list, especially when there are fewer edges compared to vertices.

Finally, edge lists are flexible and can work well with different algorithms. This includes those that deal with weighted graphs or need updates as the graph changes. Because of this flexibility, edge lists can be effectively used in many areas of computer science. So, using an edge list is often a good choice when representing graphs.