Vertex
A vertex (node) is a fundamental unit of a graph, connected to others by edges.
At a glance
Key signals
50% 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.
Enables · leads to
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.
System context
Vertexis part ofGraph data structureEstablished
Vertices are the nodes of a graph.
Mechanism: A graph is a set of vertices together with the edges that connect them.
Structural role & consequence
Interpreted from the current atlas graph — what the connections mean, not just how many there are.
50% of its relationships cross field boundaries, reaching 2 other disciplines — a cross-disciplinary connector.
structural · Structural graph analysis — not a claim of importance, causation or history.
Currently dark in the atlas: no key date stored · 2 of 2 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Structural neighbourhood: 2 → 6 → 13 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
cross-field
1 within-field, 1 cross-field
Strengths & constraints
Strengths
- Cross-disciplinary connector — 50% of its relationships cross field boundaries. structural
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
- 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
1 concept build on this directly, 3 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.
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 2 other ideas across 2 disciplines.
- A cross-disciplinary bridge — its connections reach into 2 other fields.
- Most of its connections are of the “Kind & structure” kind.
Derived from the graph’s real structure — observations, not a score.
Sources
- Vertex‐transitive graphs and vertex‐transitive maps (1991) verified
- Restricted Vertex Colorings (2008) verified