docs: remove duplicate dependency graph entries

[ChrisRackauckas-Claude]

Ignore this PR until it has been reviewed by @ChrisRackauckas.

What changed

This removes the repeated dependency-graph @docs block from the developer-only bipartite-graph page. The public APIs remain rendered in docs/src/basics/DependencyGraphs.md, their dedicated public page, which has documented this API since 2020. The internal page retains its contributor-oriented description and direct link to the owning BipartiteGraphs API.

The repeated internal block was added by bc8ebdb. A formal exact-name bisect identified 060a3fb as the first commit where Documenter sees the duplicates, because that later commit owner-qualified the older canonical entries.

Failing before

On unmodified upstream master, the local discriminator reports each binding twice:

ModelingToolkitBase.equation_dependencies=2
ModelingToolkitBase.variable_dependencies=2
ModelingToolkitBase.eqeq_dependencies=2
ModelingToolkitBase.varvar_dependencies=2
ModelingToolkitBase.asgraph=2
ModelingToolkitBase.asdigraph=2
ModelingToolkit.map_variables_to_equations=2
discriminator=FAIL

The formal bisect command was:

git bisect start f3248317cb bc8ebdb727^
git bisect run bash -c 'for name in ModelingToolkitBase.equation_dependencies ModelingToolkitBase.variable_dependencies ModelingToolkitBase.eqeq_dependencies ModelingToolkitBase.varvar_dependencies ModelingToolkitBase.asgraph ModelingToolkitBase.asdigraph ModelingToolkit.map_variables_to_equations; do count=$(grep -hFx "$name" docs/src/basics/DependencyGraphs.md docs/src/internals/bipartite_graph.md 2>/dev/null | wc -l); test "$count" -le 1 || exit 1; done'

Passing after

The same discriminator reports each binding exactly once and exits successfully.

On exact upstream f3248317cb51e08e78fb3d1729286905ad61d6d4, I ran:

DISPLAY=:0 JULIA_DEBUG=Documenter xvfb-run -a -s '-screen 0 1024x768x24' \
  julia +lts --startup-file=no --project=docs/ --code-coverage=user docs/make.jl

Documenter emitted zero duplicate diagnostics for this dependency-graph cluster. The only seven remaining duplicate diagnostics are the separate linear-analysis cluster fixed by #4977. The build exited 1 on the remaining clean-master [:docs_block, :missing_docs, :cross_references, :linkcheck] categories; link checking encountered transient remote failures.

Other local verification

git diff --check
git diff --name-only --diff-filter=ACM | rg '\.jl$' | xargs -r runic --check
git diff --no-ext-diff | typos -

These pass; there are no changed Julia files for Runic.

GROUP=QA julia +lts --startup-file=no --project -e 'using Pkg; Pkg.test()' completed with 38 pass, 4 error. The four existing clean-master ExplicitImports errors are no_implicit_imports, no_stale_explicit_imports, all_explicit_imports_via_owners, and all_qualified_accesses_via_owners.

I did not run GPU, downstream, or GROUP=Everything jobs.

Links

• Repeated block commit: bc8ebdb
• First Documenter-visible duplicate commit: 060a3fb
• Separate linear-analysis fix: docs: remove duplicate linear analysis entries #4977
• Clean-master docs job: https://github.com/SciML/ModelingToolkit.jl/actions/runs/31869817836/job/94981845495

[ChrisRackauckas-Claude]

Superseded by #4979, which contains the same duplicate dependency-graph documentation removal as part of the complete rendered-doc audit.