In my last article, we model different kinds of graphs in abstract relational databases.

We talk about hypergraphs and even model Undirected hypergraphs. Let's recap our undirected models.

Hypergraph

Undirected Hypergraph

A hypergraph is a mathematical generalization of graphs where a hyperedge could connect multiple or no nodes. So, you have a set of nodes instead of a pair of nodes. Hypergraphs are an emerging domain for modeling complex and dynamic systems and are widely used for temporal and event-dependent graphs. We will model undirected hypergraphs.

Usually, a hypergraph is drawn assets that overlap or as Vin diagrams.

As far as edges now have many-to-many relations with nodes, we just need a joint table.

Nodes

Edges

Edge to nodes

The table could increase if you have a significant edge with a comprehensive set of nodes.

Directed HyperGraph

In directed HyperGraph, we divide nodes into a subset of in-nodes and out-nodes. So, we have a directed edge from one subset to another subset.

We have multiple options for modeling this structure.

As directed, edge-node relations

The most straightforward way is to add a direction attribute to edge-node pairs.

Now Nodes and edges stay the same as in preve example

But relations now has a directions

Pros of this model

• simplicity
• ability to create mixed graphs — directed and undirected

Cons of this model

• it could be hard to build queries
• The model could encode invalid states. Nobody prevents us from having the same node on the same edge in two directions.
• for a strictly directed graph we need extra application-level constraints

As directed Graph of nodesets

We could be more explicit and extend a model from a directed graph to operate with node sets

Now, the source and object of the edge point to a node-set relation. For simplicity, we expect that in the case of individual nodes, we create separate node-set for these nodes

Pros of this model

• more explicit

Cons of this model

• Require to create a node set for single nodes
• more complex