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Is there a difference between a graph and a hypergraph database?

Is every hypergraph database system also a graph database system?

I am asking for a side-by-side comparison. If it is possible to show this in one row:

Graph support:       No/Graph/Hypergraph

Or if it is better to use two rows:

Graph support:       No/Yes
Hypergraph suppport: No/Yes

Or means "graph" and "hypergraph" the same in the database context?

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1 Answer 1

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How a certain graph database handles its edges is an implementation detail. Hence an answer cannot really be given in regards to "[hyper]graph databases in general".

From the point of mathematical graph theory however there is a difference:

  • Edges as known from standard graphs model (directed or undirected) 1:1 connections.
  • Hyperedges as known from hypergraphs model (directed or undirected) n:n connections.

Graph vs. Hypergraph:

A simple graph can be considered a special case of the hypergraph, namely the 2-uniform hypergraph. However, when stated without any qualification, an edge is always assumed to consist of at most 2 vertices, and a graph is never confused with a hypergraph. (Source)

Undirected hyperedges:

A[n] [undirected] hyperedge is an edge that is allowed to take on any number of vertices, possibly more than 2. A graph that allows any hyperedge is called a hypergraph. (Source)

Directed hyperedges:

Directed hypergraphs (Ausiello et al., 1985; Gallo et al., 1993) are a generalization of directed graphs (digraphs) and they can model binary relations among subsets of a given set. (Source)

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This is not quite correct. A hypergraph is a many to many connection, not a one to many connection. (Source) –  Regexident Nov 9 '12 at 18:02
@Regexident I was talking about the edges and not the whole hypergraph. I am not so deep into this topic but I think that makes a difference? So maybe we are both right? –  flori Nov 23 '12 at 17:08
Nope. Undirected hyperedges are just n connections (n being a set of vertices, or n:n with both n being equal sets of vertices). While directed hyperedges are n:n connections (again n being sets of vertices). –  Regexident Nov 24 '12 at 14:42
@Regexident Would be great if you could fix my answer? (I guess it's possible because it is a "community wiki"?) My understanding seems to be not deep enough yet. –  flori Nov 24 '12 at 15:38

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