~/writing/math-foundations-for-reasoning-models $ ls
Graphs and Computation
Edge
An edge is a connection between nodes in a graph.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Edge
Definition
An edge is a connection between nodes.
Example:
A -- B
This means node A is connected to node B.
Edge = connection between nodes.
Edge As Pair
An edge can be represented as a pair of nodes.
Example:
(A, B)
This says there is a connection involving A and B.
In graph language:
V = {A, B, C}
E = {(A, B), (B, C)}
V is the set of nodes.
E is the set of edges.
A graph is built from nodes plus edges.
Edge As Relation
An edge is closely related to the idea of a relation.
If a relation says:
A is connected to B
then the graph can draw that relation as an edge:
A -- B
Edges make relation structure visible.
Edge vs Node
A node is an object.
An edge is a connection between objects.
Example:
A, B, C are nodes
A -- B is an edge
B -- C is an edge
Nodes are things; edges are links between things.
Self-Loop
Sometimes an edge can connect a node to itself.
Example:
A -- A
This is called a self-loop.
It means the node has a relationship to itself.
Some graph structures allow self-connections.
Final Summary
- An edge is a connection between nodes.
- Edges can be represented as pairs.
- A graph contains nodes and edges.
- Edges are a visual form of relation structure.
- A self-loop connects a node to itself.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Directed Graph