Why are Graphs elegant?

Graphs are elegant and provide a simpler way to frame complex problems within the computer sciences domain. Graph problems are typically NP-Complete and are therefore useful for study in computational complexity. Graphs are used to model different scenarios from routing algorithms to finite state machines, and if you go into a bit more detail, you will see that graph algorithms can be parallelized in a much better way.

Google realized the importance of graphs, visualized the web as a series of connected web pages via hyperlinks, and created a competitive advantage by building the fastest search engine around.

The simplicity of Graph computation can be gauged from the fact that all the algorithms operate in the same pattern, that is, access the directly connected neighbors of a particular vertex. The beauty of this approach is that you can easily parallelize this over an MPP environment.

Consider the following graph:

You can have any particular algorithm that...