Generalizations
In a hypergraph, an edge can join more than two vertices.
An undirected graph can be seen as a simplicial complex consisting of 1-simplices (the edges) and 0-simplices (the vertices). As such, complexes are generalizations of graphs since they allow for higher-dimensional simplices.
Every graph gives rise to a matroid.
In model theory, a graph is just a structure. But in that case, there is no limitation on the number of edges: it can be any cardinal number, see continuous graph.
In computational biology, power graph analysis introduces power graphs as an alternative representation of undirected graphs.
In geographic information systems, geometric networks are closely modeled after graphs, and borrow many concepts from graph theory to perform spatial analysis on road networks or utility grids.
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