Graph Complement Edge List
Build the loop-free complement on an explicit bounded vertex set; parallel edges count as one adjacency and directed complements use ordered pairs.
Description
Build the loop-free complement on an explicit bounded vertex set; parallel edges count as one adjacency and directed complements use ordered pairs.
A graph complement contains missing connections among a declared vertex set. The directed flag determines which orientations count separately.
When to use this tool
Build the loop-free complement on an explicit bounded vertex set; parallel edges count as one adjacency and directed complements use ordered pairs.
- Prepare the supplied edgesJson, vertices, directed 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, vertices, directed. 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.edges. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate unique vertices and all edge endpoints. For each distinct vertex pair, emit it if absent; directed mode tests ordered pairs and undirected mode tests each unordered pair once, matching either source orientation.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 |
| vertices | vertices. | List of strings; at most 128 entries |
| directed | Explicit choice for directed; supply a boolean rather than a text label. | true or false |
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.edges | The edges list in the ordering and representation described above. |
{
"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}]",
"vertices": [
"u",
"v",
"w"
],
"directed": false
},
"output": {
"result": {
"edges": [
[
"u",
"w"
],
[
"v",
"w"
]
]
}
}
}Limitations and assumptions
- Self-loops are excluded from the complement. Weights and parallel multiplicities do not change whether a connection is present.
- 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
- Graph Declared Bipartition Edge Audit
Verify a supplied disjoint bipartition against each edge occurrence, reporting unknown endpoints and within-side edges rather than finding a new coloring.
- 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.