Edge
An edge is a link between two vertices of a graph; it may be directed and may carry a weight.
At a glance
Key signals
25% cross fields · reaches 2 more
- Graph Theory
- Mathematics
- Explanation
- Examples
- Misconception
- Sourced relations
- Attribution
Dependencies
What this concept builds on and what it makes possible — derived from the atlas’s dependency, causal and structural relations, not from every related edge.
Foundations · builds on
Edgedepends onVertexEstablished
An edge depends on the vertices it joins.
Mechanism: An edge is defined as an unordered (or ordered) pair of vertices; without vertices there is nothing for it to connect.
Enables · leads to
Connectivitydepends onEdgeEstablished
Connectivity is determined by which edges are present.
Mechanism: A graph is connected when its edges provide a path between every pair of vertices; adding or removing edges changes connectivity.
Shortest pathdepends onEdgeEstablished
A shortest path is built from edges.
Mechanism: A path is a sequence of edges; its length is the sum of their weights, and the shortest path minimises that sum.
System context
Edgeis part ofGraph data structureEstablished
Edges join the vertices of a graph.
Mechanism: Each edge records a relationship between two vertices, optionally with a direction and a weight.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
Currently dark in the atlas: no key date stored · 4 of 4 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 1 foundation (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Structural neighbourhood: 4 → 6 → 13 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
cross-field
3 within-field, 1 cross-field
Strengths & constraints
Constraints
- Evidence coverage currently thin in the atlas — few of its relationships carry claim-level evidence. atlas representation
- No dated history stored — the atlas records no key date for this concept. atlas representation
Conditions
- Its dependency reading rests on 1 foundation relation. structural
- Read structurally — most of its relationships carry no external evidence yet, so claims here are graph-derived. structural
Dependency radial
What this concept builds on (left) and what it makes possible (right) — derived from dependency and causal relations.
What builds on this
2 concepts build on this directly, 2 in total, across 2 disciplines.
Structural downstream reach along dependency edges — not a claim of historical necessity.
Seen through each discipline
How this concept sits in each of its fields — derived from its real connections in the graph, not asserted.
Through this lens it connects to Shortest path, Connectivity and Vertex.
Through this lens it connects to Shortest path, Connectivity and Vertex.
Related ideas to explore
Concepts that look related but are not yet connected here — candidates for a connection to reason about, not established links.
This idea also appears in…
The same structure shows up in other disciplines. These are real recurrences drawn from the graph — a starting point for asking “what carries over, and what changes?”
Concepts
crosses a discipline boundary
- Connects 4 other ideas across 2 disciplines.
- A cross-disciplinary bridge — its connections reach into 2 other fields.
- Most of its connections are of the “Dependency” kind.
Derived from the graph’s real structure — observations, not a score.