Graph Line Adjacency Builder
Build undirected line-graph adjacency between distinct edge occurrences sharing endpoints; original edge IDs become vertices and loops do not create line self-loops.
Description
Build undirected line-graph adjacency between distinct edge occurrences sharing endpoints; original edge IDs become vertices and loops do not create line self-loops.
An undirected line graph represents original edges as vertices and joins edges sharing an endpoint.
When to use this tool
Build undirected line-graph adjacency between distinct edge occurrences sharing endpoints; original edge IDs become vertices and loops do not create line self-loops.
- 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.vertices, result.edges. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Use each unique original edge ID as a new vertex. For every distinct source-edge pair, emit an ID pair if either endpoint is shared, ignoring original direction.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.vertices | The vertices list in the ordering and representation described above. |
| 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}]"
},
"output": {
"result": {
"vertices": [
"a",
"b",
"c"
],
"edges": [
[
"a",
"b"
],
[
"a",
"c"
],
[
"b",
"c"
]
]
}
}
}Limitations and assumptions
- No self-adjacency is emitted. This is the declared undirected incidence model even when the original records have direction, loops or parallel edges.
- 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
- adjacency list to matrix
Convert an adjacency map into a square 0/1 matrix with sorted node order.
- adjacency matrix to list
Convert a square 0/1 adjacency matrix into an adjacency map of sorted neighbor lists.