Personal Knowledge MetaGraphs in Relational Model for AI Agents Memory
I started a long series of articles about how to model different types of knowledge graphs in the relational model, which makes on-device memory models for AI agents possible.
We model-directed graphs
Also, graphs of entities
We even model hypergraphs
Last time, we discussed why classical triple and simple knowledge graphs are insufficient for AI agents and complex memory, especially in the domain of time-aware or multi-model knowledge.
So why do we need metagraphs, and what kind of challenge could they help us to solve?
- complex and nested event and temporal context and temporal relations as edges
- multi-mode and multilingual knowledge
- human-like memory for AI agents that has multiple contexts and relations between knowledge in neuron-like networks
MetaGraphs
A meta graph is a concept that extends the idea of a graph by allowing edges to become graphs. Meta Edges connect a set of nodes, which could also be subgraphs. So, at some level, node and edge are pretty similar in properties but act in different roles in a different context.
Also, in some cases, edges could be referenced as nodes.
This approach enables the representation of more complex relationships and hierarchies than a traditional graph structure allows. Let’s break down each term to understand better metagraphs and how they differ from hypergraphs and graphs.
Graph Basics
- A standard graph has a set of nodes (or vertices) and edges (connections between nodes).
- Edges are generally simple and typically represent a binary relationship between two nodes.
- For instance, an edge in a social network graph might indicate a “friend” relationship between two people (nodes).
Hypergraph
- A hypergraph extends the concept of an edge by allowing it to connect any number of nodes, not just two.
- Each connection, called a hyperedge, can link multiple nodes.
- This feature allows hypergraphs to model more complex relationships involving multiple entities simultaneously. For example, a hyperedge in a hypergraph could represent a project team, connecting all team members in a single relation.
- Despite its flexibility, a hypergraph doesn’t capture hierarchical or nested structures; it only generalizes the number of connections in an edge.
Metagraph
- A metagraph allows the edges to be graphs themselves. This means each edge can contain its own nodes and edges, creating nested, hierarchical structures.
- In a meta graph, an edge could represent a relationship defined by a graph. For instance, a meta graph could represent a network of organizations where each organization’s structure (departments and connections) is represented by its own internal graph and treated as an edge in the larger meta graph.
- This recursive structure allows metagraphs to model complex data with multiple layers of abstraction. They can capture multi-node relationships (as in hypergraphs) and detailed, structured information about each relationship.
Named Graphs and Graph of Graphs
As you can notice, the structure of a metagraph is quite complex and could be complex to model in relational and classical RDF setups. It could create a challenge of luck of tools and software solutions for your problem.
If you need to model nested graphs, you could use a much simpler model of Named graphs, which could take you quite far.
The concept of the named graph came from the RDF community, which needed to group some sets of triples. In this way, you form subgraphs inside an existing graph. You could refer to the subgraph as a regular node. This setup simplifies complex graphs, introduces hierarchies, and even adds features and properties of hypergraphs while keeping a directed nature.
It looks complex, but it is not so hard to model it with a slight modification of a directed graph.
So, the node could host graphs inside. Let's reflect this fact with a location for a node. If a node belongs to a main graph, we could set the location to null or introduce a main node . it is up to you
Nodes could have edges to nodes in different subgraphs. This structure allows any kind of nesting graphs. Edges stay location-free
Meta Graphs in Relational Model
Let’s try to make several attempts to model different meta-graphs with some constraints.
Directed Metagraph where edges are not used as nodes and could not contain subgraphs
In this case, the edge always points to two sets of nodes. This introduces an overhead of creating a node set for a single node. In this model, we can model empty node sets that could require application-level constraints to prevent such cases.
Directed Metagraph where edges are not used as nodes and could contain subgraphs
Adding a node set that could model a subgraph located in an edge is easy but could be separate from in-vertex or out-vert.
I also do not see a direct need to include subgraphs to a node, as we could just use a node set interchangeably, but it still could be a case.
Directed Metagraph where edges are used as nodes and could contain subgraphs
As you can notice, we operate all the time with node sets. We could simply allow the extension node set to elements set that include node and edge IDs, but in this case, we need to use uuid or any other strategy to differentiate node IDs from edge IDs. In this case, we have a collision of ephemeral edges or ephemeral nodes when we want to change the role and purpose of the node as an edge or vice versa.
A full-scale metagraph model is way too complex for a relational database.
So we need a better model.
Now, we have more flexibility but loose structural constraints. We cannot show that the element should have one vertex, one vertex, or both. This type of constraint has been moved to the application level. Also, the crucial question is about query and retrieval needs.
Any meta-graph model should be more focused on domain and needs and should be used in raw form. We did it for a pure theoretical purpose.
