chore: add documentation for the weighted graph

[senojj]

Description

Document some of the rules that govern the weighted authorization graph.

References

Review Checklist

• I have clicked on "allow edits by maintainers".
• I have added documentation for new/changed functionality in this PR or in a PR to openfga.dev [Provide a link to any relevant PRs in the references section above]
• The correct base branch is being used, if not main
• I have added tests to validate that the change in functionality is working as expected

Summary by CodeRabbit

• Documentation
  • Added comprehensive documentation for weighted authorization graphs.
  • Clarified vertex and edge types, structural constraints, naming rules, and permitted endpoints.
  • Documented weight propagation, sink reachability, tuple resolution, logical groupings, and recursive or tuple cycles.
  • Added guidance for direct, intersection, and exclusion paths, including cycle restrictions and finiteness guarantees.

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Walkthrough

Changes

Weighted authorization graph

Layer / File(s)	Summary
Graph specification pkg/go/graph/README.md	Defines vertex and edge kinds, naming and structural constraints, edge conditions, grouping, weight propagation, sink reachability, tuple-resolving edges, circulation rules, and recursive tuple cycles.
Graph theorems pkg/go/graph/README.md	States nine theorems about path weights, circulation, terminal targets, reachability, expression trees, intersections, exclusions, and global finiteness bounds.

Estimated code review effort: 2 (Simple) | ~10 minutes

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and concisely describes the main change: adding documentation for the weighted authorization graph.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests
• Commit unit tests in branch chore/weighted-graph-documentation

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Actionable comments posted: 4

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@pkg/go/graph/README.md`:
- Line 49: Correct the exclusion weight rule in the README statement: when the
base edge reaches the sink, a successful subtract branch must suppress the base
result and produce weight zero; do not describe the result as max(base,
subtract).
- Around line 45-48: Clarify the weight definitions in the README by defining
how outgoing-edge contributions are derived from vertex weights, and revise the
edge monotonicity rule to apply only to edges that contribute to propagation.
Ensure the intersection rule permits a zero vertex weight when an outgoing edge
cannot reach the sink, without contradicting the monotonicity rule; use explicit
operator exceptions if propagation-scoped wording is insufficient.
- Line 27: Update Axiom 4 in the graph README to apply only to represented or
existing source, target, kind, and tupleset-relation combinations, rather than
requiring an edge for every possible combination. Preserve the uniqueness and
condition-accumulation requirements for combinations that do exist.
- Line 15: Update the reachability definition in the graph README to describe an
operator-aware, tuple-valid path rather than any directed path, ensuring it
accounts for tuple resolution and branch rejection required by Axioms 44 and 48.
Revise the later weight rules to use this propagation-valid reachability
definition consistently.

🪄 Autofix

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
• Create a new PR with the fixes

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Run ID: af6f29a0-42b5-4488-9dac-478a90a5053c

📥 Commits

Reviewing files that changed from the base of the PR and between b86b212 and 1ea7618.

📒 Files selected for processing (1)

• pkg/go/graph/README.md