Implementing graph representations like adjacency matrices, adjacency lists, and edge lists can be tricky in real-world situations. This is because real-world data can be quite complicated. Real-world graphs can be huge, with millions of points (or nodes) and connections (or edges). The way we choose to represent these graphs can really affect how well they work and how easy they are to use.

Let’s start with space efficiency. An adjacency matrix uses a lot of space: it needs $O(V^2)$, where $V$ is the number of vertices. This can be a waste, especially for sparse graphs, where there aren't many edges compared to the total number of possible edges. On the other hand, an adjacency list takes up less space, based on the actual number of edges: it only needs $O(E)$. Picking the wrong way to represent a graph can mean wasting memory or making things slower.

Now, let’s talk about time complexity. This is about how long it takes to do certain tasks. For example, checking if there’s a connection between two nodes takes $O(1)$ time with an adjacency matrix, but it takes $O(V)$ time with an adjacency list because you have to look through the list. On the flip side, finding all the edges is faster with an adjacency list: that takes $O(E)$, while with an adjacency matrix, it takes $O(V^2)$. This means you have to think about what tasks you will do the most in your application so you can choose the best representation.

Another point to consider is that graphs can change. You might need to add or remove nodes and edges. An adjacency list usually handles these changes better because adding or removing items just requires changing some pointers. But with an adjacency matrix, you might need to resize it, which can slow things down. If your graph changes a lot, this could be a problem.

There are also algorithm considerations. Different graph representations can lead to different complexities when running algorithms like Dijkstra's or Depth-First Search (DFS). For instance, BFS works better with an adjacency list, while using an adjacency matrix could slow it down because of extra steps involved.

Lastly, real-world data can have noise or problems that don't fit well with these representations. If there are outliers or missing data, you might need to do extra work to prepare the data before using it, which can make things even more complicated.

In summary, picking the right way to represent a graph is important—it’s not just an academic task. You need to really understand what your application needs, what the data is like, and what limits you might face. Finding a balance between efficiency, flexibility, and performance is key to making sure your system can handle the complexities of real-world graph data.