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After reading Stevey Yegge's Get That Job At Google article, I found this little quote interesting:
Whenever someone gives you a problem, think graphs. They are the most fundamental and flexible way of representing any kind of a relationship, so it's about a 50–50 shot that any interesting design problem has a graph involved in it. Make absolutely sure you can't think of a way to solve it using graphs before moving on to other solution types. This tip is important!
What are some examples of problems that are best represented and/or solved by graph data structures/algorithms?
One example I can think of: navigation units (ala Garmin, TomTom), that supply road directions from your current location to another, utilize graphs and advanced pathing algorithms.
What are some others?
Analysing transaction serialisability in database theory.