For most graphs, each node is meant to represent an object and an edge is meant to be pairwise relationship between two nodes.
Since an edge is a relationship between two nodes, and we can think of nodes as points, each edge is a line.
However, are there instances where we might need to perform more than pairwise relationships between nodes? For example, what if there existed a type of relationship that only makes sense between a set of 3 nodes. If this were the case, then the edge representing this relationship must span 3 nodes and exist as a plane connecting all 3 as opposed to a line.
Are there any examples of this type of graph? Any applications? I was just thinking about this and couldn't find any work on this. Thanks!
What you're describing is called a hypergraph.