+++
title = "Fix graph orientation: show goals at root, prerequisites as leaves"
priority = 7
status = "done"
ticket_type = "bug"
dependencies = []
+++
## Problem

The dependency graph is inverted. Currently:
- **Roots** = tickets with no dependencies (foundation/leaf-level work)
- **Children** = dependents of the root (tickets blocked by it)

This means the graph reads bottom-up: you see "what blocks what" rather than "what needs what".

## Desired behavior

If ticket A depends on B, C, and D:
- `nbd graph` should show A at the top with B, C, D indented as children (leaves)
- Roots = tickets with **no dependents** (nobody depends on them — these are the top-level goals)
- Children = the **dependencies** of the current node (prerequisites)

This makes the graph read naturally: goals at the top, work to be done first at the bottom.

## Files to change

### `src/graph.rs`

- `roots()`: change predicate from `node.dependencies.is_empty()` to `node.dependents.is_empty()`
- `subtree()` + `dfs_subtree()`: currently traverses `dependents` edges; should traverse `dependencies` edges so subtree(A) returns A + what A depends on (recursively)
- `to_json_value()` and `to_subtree_json_value()`: edge direction in JSON output should be `{"from": dependent_id, "to": dependency_id}` (A→B means A depends on B), or reconsider the `from`/`to` labels in light of the new orientation
- Update all doc comments to reflect the new semantics

### `src/display.rs`

- `render_node()`: iterate `node.dependencies` as children (not `node.dependents`)
- Update doc comments for `format_graph()` and `format_subtree()`

### `src/graph.rs` module-level doc comment

The edge semantics paragraph should be updated: "A is a dependency of B" means A appears as a child in the tree of B.

### Tests

Update any graph-related tests in `src/tests.rs` and `tests/integration.rs` that assert the current (inverted) traversal order.