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It's not so much that we want to model problems as graphs, it's that many problems and situations naturally correspond to graphs. Anything with a collection of

It's not so much that we want to model problems as graphs, it's that many problems and situations naturally correspond to graphs. Anything with a collection of objects, where some subset of pairs of objects are "related" to each other, is a graph. In mathematical terms, graphs are essentially the same as binary relations on a set (a generalization of functions). And any time you can think of something as a graph, you can benefit from the wealth of available mathematical and computational tools that apply to all graphs.

eru 2y ago
Graphs are also really simple structures mathematically. After all, an (undirected) graph is nothing more than a ground set and a collection of its two-element subsets. It's the same reason why groups crop up so often: groups are also really simple structures, so it's really easy to satisfy their axioms 'by accident'. Same for numbers in general.
- whatshisface 2y ago
  I don't think that's a full explanation for groups, because groups other than the free or permutation groups are rather "unlikely," in the sense that they're much smaller.
  - eru 2y ago
    Oh, I mean they crop up in lots and lots of applications, because their structure is so simple to satisfy. Not that they would crop up, if you somehow randomly generated mathematical structure. The real world, and especially the part of the real world that people engage with, seems to have a lot of simple structures.
ForTheKidz 2y ago
Graphs don't really capture the entirety of hashmaps and other indexing concerns. Other than that yea I agree.
- magicalhippo 2y ago
  GP was talking about modelling your problem. A hashmap is seldom a good model for a given problem. Typically they're "just" an implementation detail. For example, in some cases it can be useful to consider triangles in a 3D model as cyclic graphs of vertices. The edges of the triangle correspond to the edges in the graph. However I can't think of any case where it's useful to think of a triangle as a hashmap.

eru 2y ago

Graphs are also really simple structures mathematically. After all, an (undirected) graph is nothing more than a ground set and a collection of its two-element subsets. It's the same reason why groups crop up so often: groups are also really simple structures, so it's really easy to satisfy their axioms 'by accident'. Same for numbers in general.

whatshisface 2y ago
I don't think that's a full explanation for groups, because groups other than the free or permutation groups are rather "unlikely," in the sense that they're much smaller.
- eru 2y ago
  Oh, I mean they crop up in lots and lots of applications, because their structure is so simple to satisfy. Not that they would crop up, if you somehow randomly generated mathematical structure. The real world, and especially the part of the real world that people engage with, seems to have a lot of simple structures.

ForTheKidz 2y ago

Graphs don't really capture the entirety of hashmaps and other indexing concerns. Other than that yea I agree.

magicalhippo 2y ago
GP was talking about modelling your problem. A hashmap is seldom a good model for a given problem. Typically they're "just" an implementation detail. For example, in some cases it can be useful to consider triangles in a 3D model as cyclic graphs of vertices. The edges of the triangle correspond to the edges in the graph. However I can't think of any case where it's useful to think of a triangle as a hashmap.