A hyper edge is defined as follows:

A hyperedge is a connection between two or more vertices, or nodes, of a hypergraph. A hypergraph is a graph in which generalized edges (called hyperedges) may connect more than two nodes with discrete properties.

In Neo4j, an edge (or relationship) can only be between itself or another node; there’s no way of creating a relationship between more than 2 nodes.

I had problems when trying to model the relationship between a player and a football match because I wanted to say that a player participated in a match and represented a specific team in that match.

I started out with the following model:

Unfortunately, creating a direct relationship from the player to the match means that there’s no way to work out which team they played for.

This information is useful because sometimes players transfer teams in the middle of a season and we want to analyze how they performed for each team.

In a property graph, we need to introduce an extra node which links the match, player and team together:

Although we are forced to adopt this design it actually helps us realize an extra entity in our domain which wasn’t visible before – a player’s performance in a match.

If we want to capture information about a players’ performance in a match we can store it on this node.

We can also easily aggregate players stats by following the played relationship without needing to worry about the matches they played in.

The Neo4j manual has a few more examples of domain models containing hyper edges which are worth having a look at if you want to learn more.