Edge List Degree Sum Audit
Audit degree-sum identities on occurrence-preserving directed edges; loops contribute twice to undirected degree and parallel occurrences count.
Description
Audit degree-sum identities on occurrence-preserving directed edges; loops contribute twice to undirected degree and parallel occurrences count.
Degree accounting treats a self-loop differently in directed and undirected counts. Keeping all totals makes the convention visible.
When to use this tool
Audit degree-sum identities on occurrence-preserving directed edges; loops contribute twice to undirected degree and parallel occurrences count.
- Prepare the supplied edgesJson fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter edgesJson. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.degrees, result.inSum, result.outSum, result.undirectedSum, result.edgeCount. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
For each observed endpoint label count incoming, outgoing and undirected incidences, with loops adding one to each directed count and two to undirected degree. Return per-vertex counts, their sums and edgeCount.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| edgesJson | JSON text, entered as one text field. The decoded structure is illustrated below; it is not a separate file. | Text |
For the JSON text fields, the following decoded structures show the example records before they are serialized into input strings. Keep field names, list nesting and value types as shown.
[
{
"field": "edgesJson",
"decoded": [
{
"id": "a",
"source": "u",
"target": "v",
"weight": 2
},
{
"id": "b",
"source": "v",
"target": "u",
"weight": 4
},
{
"id": "c",
"source": "u",
"target": "u",
"weight": 1
}
]
}
]| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.degrees | The degrees list in the ordering and representation described above. |
| result.inSum | The in sum value under the stated formula or text convention. |
| result.outSum | The out sum value under the stated formula or text convention. |
| result.undirectedSum | The undirected sum value under the stated formula or text convention. |
| result.edgeCount | The edge count value under the stated formula or text convention. |
{
"input": {
"edgesJson": "[{\"id\":\"a\",\"source\":\"u\",\"target\":\"v\",\"weight\":2},{\"id\":\"b\",\"source\":\"v\",\"target\":\"u\",\"weight\":4},{\"id\":\"c\",\"source\":\"u\",\"target\":\"u\",\"weight\":1}]"
},
"output": {
"result": {
"degrees": [
{
"vertex": "u",
"incoming": 2,
"outgoing": 2,
"undirected": 4
},
{
"vertex": "v",
"incoming": 1,
"outgoing": 1,
"undirected": 2
}
],
"inSum": 3,
"outSum": 3,
"undirectedSum": 6,
"edgeCount": 3
}
}
}Limitations and assumptions
- Isolated vertices absent from all edges cannot appear in this inferred vertex list. Weights are ignored and parallel edges each contribute.
- Every edge record requires unique string id, string source/target and finite numeric weight, even when this operation does not use the weight. Parallel endpoints and loops are retained unless explicitly filtered.
- Every declared top-level field is required and unexpected fields are rejected. Numeric inputs must be finite; ordinary text fields are bounded to 8,192 UTF-16 code units, with tighter operation-specific limits where stated.
- Lists are limited to 128 entries. JSON text must meet bounded size and depth checks, and numeric outputs beyond the safe finite magnitude are rejected. Exact large integers use decimal strings.
- Indexes are zero-based and spans have an exclusive end unless explicitly stated otherwise. A valid false, null or empty-list result is distinct from malformed input.
Alternative or Complementary methods
Choose edge identities, directedness and vertex coverage explicitly. Local edge-list audits and transformations do not replace a graph algorithm with the required connectivity, path or ordering guarantees.
References
Similar or alternative tools
- Edge ID Trail Validity Check
Verify an edge-ID trail with no repeated edge occurrences from an explicit start; directed or undirected traversal, with failure indexes retained.
- Edge List Boundary Cut Selector
Select edges crossing an explicit vertex-set boundary using endpoint exclusive membership; direction and occurrence IDs remain intact.