Description
Return nodes-1-degree as remainingNeighbors and feasible when degree is below nodes.
A graph's degree records how many edge incidences meet a vertex. Directed edges distinguish incoming and outgoing incidences, while loops and parallel edges require explicit counting conventions; a local degree formula does not reconstruct a graph.
Return nodes-1-degree as remainingNeighbors and feasible when degree is below nodes.
When to use this tool
Use Graph Degree Sequence Single Node Budget when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter nodes, degree. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingNeighbors, feasible. Inspect feasible before interpreting the associated values.
Require positive integer nodes and nonnegative degree. Return nodes-1-degree as remainingNeighbors and feasible when degree is below nodes.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| nodes | Nodes | Required. Safe integer; minimum 1. |
| degree | Degree | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingNeighbors | Remaining Neighbors | Required. Safe integer. |
| feasible | Feasible | Required. Boolean. |
{
"input": {
"nodes": 6,
"degree": 3
},
"output": {
"remainingNeighbors": 2,
"feasible": true
}
}Limitations and assumptions
- Negative remaining capacity is retained; this necessary simple-graph local bound does not establish a graphical degree sequence, connectivity, or actual neighbors.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Build an adjacency structure and count actual incidences when a full graph is available. Validate loop, multiplicity, direction, and vertex-set assumptions before applying a simple-graph identity.
References
Similar or alternative tools
- Graph Join Isolated Node Degree Shift
Invoke the linked join increment calculator for both original and added vertices.
- Graph Join One Node Degree Increment
Return their sum and otherVertices as increment.