What are good examples of problems that graphs can solve better than the alternative? [closed]

Answer 1

The following are based on graph theory:

• Binary trees and other trees such as Red-black trees, splay trees, etc.
• Linked lists
• Anything that's modelled as a state machine (GUIs, network stacks, CPUs, etc)
• Decision trees (used in AI and other applications)
• Complex class inheritance

Answer 2

Analysing transaction serialisability in database theory.

Answer 3

Graphs are great for managing dependencies.

I recently started to use the Castle Windsor Container, after inspecting the Kernel I found a GraphNodes property. Castle Windsor uses a graph to represent the dependencies between objects so that injection will work correctly. Check out this article.

I have also used simple graph theory to develop a plugin framework, each graph node represent a plugin, once the dependencies have been defined I can traverse the graph to create a plugin load order.

I am planning on changing the algorithm to implement Dijkstra's algorithm so that each plugin is weighted with a specific version, thus a simple change will only load the latest version of the plugin.

I with I had discovered this sooner. I like that quote "Whenever someone gives you a problem, think graphs." I definitely think that's true.

Answer 4

Anything that can be modelled as a foreign key in a relational database is essentially an edge and nodes in a graph.

Maybe that will help you think of examples, since most things are readily modelled in a RDBMS.

Answer 5

Well, many program optimization algorithms that compilers use are based on graphs (e.g., figure out call graph, flow control, lots of static analysis).

Many optimization problems are based on graph. Since many problems are reducable to graph colouring and similar problems, then many other problems are also graph based.

I'm not sure I agree that graphs are the best way to represent every relation and I certainly try to avoid these "got a nail, let's find a hammer" approaches. Graphs often have poor memory representations and many algorithms are actually more efficient (in practice) when implemented with matrices, bitsets, and other things.

Answer 6

You could take a look at some of the examples in the Neo4j wiki,

http://wiki.neo4j.org/content/Domain_Modeling_Gallery

and the projects that Neo4j is used in (the known ones)

http://wiki.neo4j.org/content/Neo4j_In_The_Wild .

Otherwise, Recommender Algorithms are a good use for Graphs, see for instance PageRank, and other stuff at

https://github.com/tinkerpop/gremlin/wiki/pagerank