Shortest path
The shortest path between two vertices is the route of least total edge weight; algorithms like Dijkstra's find it efficiently.
At a glance
Key signals
33% 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
Shortest pathrequiresConnectivityEstablished
A finite shortest path requires the endpoints to be connected.
Mechanism: If two vertices lie in different connected components no path joins them, so no shortest path exists.
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.
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 · 3 of 3 of its relations lack claim-level evidence.
atlas representation · Describes the current Thinking OS representation, not the state of the world.
Builds on 2 foundations (requires / depends-on / derived-from / emerges-from).
structural · Structural graph analysis — not a claim of importance, causation or history.
Structural neighbourhood: 3 → 6 → 13 concepts reachable within 3 hops.
structural · Structural reach — being reachable is not the same as being understood.
cross-field
2 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 2 foundation relations. 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.
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 Edge and Connectivity.
Through this lens it connects to Edge and Connectivity.
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 3 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.
Sources
- Shortest path algorithms (2027) verified
- "-Approximation Schemes for the Constrained Shortest Path Problem (2016) verified