When working with graphs (the nodes and edges kind) on a computer, good arrangement and layout of the nodes is an interesting problem. To us, there is usually an obvious or at least visually appealing way to draw a graph, but a computer has no intuition (yet?) so finding a good layout for the graph can be difficult. It isn't hard to represent a graph as such in a computer, in fact things like adjacency matrices are probably much easier for a computer to read than a human, especially as you add more nodes.

There's also the problem of deciding what sort of layout is the right one for a given graph in the first place: Say you want to plot three things: A mesh network, a tree graph and a import/export relations between countries. Should each be laid out according to the same rules? Probably not - in a mesh network, we do not expect edges that reach far from one side of the graph to the other, so we can generally just place adjecent(in the sense that they are connected) nodes adjacent(location) to each other. A tree graph has a much different structure, in fact as the name implies, we would choose a tree-like layout. Import/export routes would of course be graphed according to actual geographical location, and even if not, the nodes are connected much differently. You might also want to assign a heavier weight or larger size to some nodes (according to GDP, for example).

For all of these, one can create different algorithms that find a good, or even optimal layout. Wikipedia actually has a page about some of them.

You may remember that I briefly wrote about a project I was considering, namely an interactive Wikipedia (or other webpages, for that matter) grapher. The idea is this: you give the program a starting page, and it then represents this page as a single node. When you then click it, the page is parsed for links to other Wikipedia articles, and each is added as a node on the graph, with an edge to the original article. You can repeat this process for each new node, and edges are added whenever one article links to another one on the graph.

I've started working on this project recently, and have found a good (but unfortunately somewhat slow - about O(n^3) ) algorithm to draw this graph. Force-based layout creates a layout by treating each edge as a spring that pulls adjacent nodes together, while simultaneously repulsing all nodes from each other using something resembling Coulomb's law, and then iterating until an equilibrium of forces is found. For now, I've only implemented a rough version of this algorithm in Python, but for the final program I'll be using C++, mainly to get better performance for the graphing, but also to gain a bit more experience with it. The drawing will probably be done in SDL, it seems simple enough to use.

Source code of the above animation's algorithm (graph was generated randomly):