![[Pasted image 20250314141620.png]]
A graph is a general term for a structure consisting of nodes connected by zero-to-many edges.
They are (at least in my opinion, and possibly factually verifiable) the most versatile means of organizing information. [[Everything can be represented in a graph]] - i.e. graphs can recreate _any_ other form of data structure (e.g. [[Hierarchy]] or [[Relational Databases]]).
This versatility is the graph's killer feature, but also perhaps its Achilles heel. There's no wrong way to do a graph, and because they are so flexible and general it is hard to write efficient tools that operate in such a flexible structure. Many things you **could** do in a graph are better optimized by things like [[Relational Databases]].
Graphs are stored in [[Graph Database]]s.
[[Graph Theory]] is the branch of mathematics having to do with the study of graphs.
**Misc facts:**
- Graphs can be directed (a directed graph is a "digraph"), or undirected.
- If nodes and edges have properties, then it's commonly called a [[Property Graph]]
- Directed graphs may be cyclic (you can draw a loop using edges), or [[DAG|acyclic]] (where no loops exist).
- [[Resource Description Framework|RDF]] is essentially a graph structure - node, node, edge.
- Allowed nodes & edges in a graph are its [[Ontology]].
- More complex relations are possible through the use of hyperedges & edge nodes
- **Hyperedge** - in "[[Hypergraph]]s", an edge connecting >2 nodes
- Edge Node - an edge that acts like a node, can be connected to by other edges and/or have its own properties
- [[Wikidata]] uses edge nodes
- You can represent a graph using an [[Adjacency Matrix]]
# Constructing a Graph
You can create an arbitrary graph structure using [[JSON]].
```json
{
nodes: [
{
id: "A",f
label: "Aaron",
// any other arbitrary data
type: "human",
age: 36,
},
{
id: "B",
label: "Loki",
type: "cat"
// nodes may or may not be forced to have the same set of properties
}
],
edges: [
{
from: "A",
to: "B",
label: "Owns"
}],
}
```
Doing this, though, introduces interpretation errors. This actually makes for a perfect lead-in to the concept of [[Ontology]] engineering and [[Resource Description Framework]]. In short, those concepts remove ambiguity by pointing to globally unique [[URI]]s that define properties in unambiguous terms. It also introduces conventions like prefixing known, important properties with "@", like in the example below.
```JSON
{
"@context": {
"foaf": "http://xmlns.com/foaf/spec/"
},
"@graph": [
{
"@id": "https://example.org/my-profile", // Your unique identifier
"@type": "foaf:Person",
"foaf:name": "Your Name",
"foaf:mbox": "mailto:
[email protected]" // Example FOAF property
}
]
}
```
Also demonstrated in that example is the aliasing of known ontological source prefixes. There `foaf` used in the graph is an alias for the text referred to in by the `foaf` key in the @context.
## Other graph constructions
You don't have to use [[JSON]]. You could construct a graph using [[CSV]] files, like how [[Archi]] exports work. There is also [[Turtle]] and, more generally, the [[Resource Description Framework]].
### CSV File Example
A full & arbitrarily complex [[Property Graph]] in 3 csv files.
**nodes.csv**
```csv
id, arbitrary_other_fields, ...
a, Aaron, ...
b, Bob, ...
```
**edges.csv**
```csv
id, from, to, arbitrary_other_fields, ...
ab, a, b, Aaron knows bob, ...
```
**props.csv**
```csv
id, key, val
a, age, 37
a, gender, male
b, age, 39
b, gender, male
ab, since, 2022
```
# Graphs in the Wild
- Graphs are behind so-called "friend of a friend" recommendation algorithms
- The [[JavaScript]] visualization library "GoJS" and VisJS use graph structures for their visualizations
- The productivity product **Asana** credits their graph-based approach for how to scale work-related - see [[Asana Work Graph]]
- A crazy amount of [[Diagram Types (index)|diagrams]] are just graphs - e.g.
- [[Graph Visual Representation|Petri Net]], [[IDEF0]], [[IDEF3]], [[Flow Charts]], [[State Diagrams|State Machine Diagrams]] and essentially every form of [[SysML]], [[UML]], and [[Archimate]] diagram[^1]
****
# More
## Source
- Self/experience
- Bit of Gemini, for the RDF syntax
- https://guides.sharafat.co.uk/documents/Graph_Theory_for_Dummies.pdf
## Related
[^1]: If you allow for containment being represented using a graph structure, that is. [[Archi]] and Archimate natively support this.