Typically people think of RDF as graph. But it is actually a subject of research on how to represent RDF as formal Graph.

I will show examples of RDFs and how they would be represented as formal graph if we do naive “transformation”.

See: A Comparative Study on Representing RDF as Graph and Hypergraph Data Model.

## Directed graph

RDF

```
:a → ex:1 → :b
:c → ex:1 → :d
```

Graph

```
flowchart LR
:a --> ex:1 --> :b
:c --> ex:1 --> :d
```

Not quite what we want - we can’t distinguish that there is no connection between `:a`

and `:d`

.

## Directed labeled graph

RDF

```
:a → ex:1 → :b
ex:1 → ex:2 → :d
```

Graph

```
flowchart LR
:a -- ex:1 --> :b
c[ex:1] -- ex:2 --> :d
```

Not quite what we want - we can’t use label as start (or end) of an edge.

## Bipartite graph

See: Bipartite Graphs as Intermediate Model for RDF-star, Inductive Triple Graphs: A purely functional approach to represent RDF

RDF

```
:a → ex:1 → :b
ex:1 → ex:2 → :d
```

Graph

```
flowchart LR
classDef red fill:red
classDef blue fill:blue
e1:::red
e2:::red
:a:::blue
:b:::blue
:d:::blue
x:::blue
y:::blue
e1 -- s --> :a
e1 -- p --> x[ex:1]
e1 -- o --> :b
e2 -- s --> x[ex:1]
e2 -- p --> y[ex:2]
e2 -- o --> :d
```

Some observations:

- it is bipartite graph
- but also directed labeled graph with only three labels:
`s`

- subject`p`

- predicate`o`

- object

- It is also visually reminds standard RDF reification
- but it looks nothing like what original RDF “graph”

## Directed hypergraph

See: Directed hyper-graphs for RDF documents

To be precise it is 3-unifor F-hypergraph with additionally defined function(s), which tells which node is subject, object and tail (on the graph I use edge labels to denote this, but this is for visual purposes only, this is no labeled graph)

RDF:

```
:a → ex:1 → :b
ex:1 → ex:2 → :d
```

Graph:

```
flowchart TD
:a -- s --- e1( ) -- o --> :b
ex:1 -- p --- e1
ex:1 -- s --- e2( ) -- o --> :d
ex:2 -- p --- e2( )
```

as bipartite graph

```
flowchart TD
classDef red fill:red
classDef blue fill:blue
e1:::red
e2:::red
:a:::blue
:b:::blue
:d:::blue
x:::blue
y:::blue
:a -- s --> e1 -- o --> :b
x[ex:1] -- p --> e1
x[ex:1] -- s --> e2 -- o --> :d
y[ex:2] -- p --> e2
```

## The Labeled Directed Multigraph with Triple Nodes (LDM-3N)

See: A Formal Graph Model for RDF and Its Implementation

RDF:

```
:a → ex:1 → :b
ex:1 → ex:2 → :d
```

```
flowchart LR
:a --"e1(I)"--> ex:1 --"e1(T)"--> :b
ex:1 --"e2(I)"--> ex:2 --"e2(T)"--> :d
```

RDF triple is splitted into two labeled edges - they get same unique suffix and one of two suffixes: `I`

stands for initial, `T`

stands for terminal.