# `Yog.Layout.Multipartite`
[🔗](https://github.com/code-shoily/yog_ex/blob/v1.0.0/lib/yog/layout/multipartite.ex#L1)

Multipartite layout algorithm for positioning graph nodes in parallel layers.

Arranges nodes in straight parallel lines (either vertical columns or horizontal rows)
based on their partition/layer membership. This layout is standard for bipartite
graphs, feedforward neural network visualizations, flow networks, or any layered
hierarchical relationships.

## Mathematical Model

Given a list of layers $L = [L_0, L_1, \dots, L_{M-1}]$, where each $L_j$ is a list of node IDs, a bounding space of size $W \times H$, and center $(c_x, c_y)$:

If `:align` is `:vertical` (default):
1. The $x$-coordinate for all nodes in layer $L_j$ is:
   $$x_j = \left(c_x - \frac{W}{2}\right) + \frac{j \cdot W}{M - 1}$$
   (or $c_x$ if $M = 1$).
2. For the $i$-th node in layer $L_j$ (where $0 \le i < K$ and $K = |L_j|$):
   $$y_i = \left(c_y - \frac{H}{2}\right) + \frac{i \cdot H}{K - 1}$$
   (or $c_y$ if $K = 1$).

If `:align` is `:horizontal`:
1. The $y$-coordinate for all nodes in layer $L_j$ is:
   $$y_j = \left(c_y - \frac{H}{2}\right) + \frac{j \cdot H}{M - 1}$$
   (or $c_y$ if $M = 1$).
2. For the $i$-th node in layer $L_j$ (where $0 \le i < K$ and $K = |L_j|$):
   $$x_i = \left(c_x - \frac{W}{2}\right) + \frac{i \cdot W}{K - 1}$$
   (or $c_x$ if $K = 1$).

## Complexities

* **Time Complexity:** $O(V)$ where $V$ is the number of nodes.
* **Space Complexity:** $O(V)$ auxiliary space.

# `layout`

```elixir
@spec layout(Yog.Graph.t() | Yog.DAG.t(), [[Yog.Graph.node_id()]], keyword()) :: %{
  required(Yog.Graph.node_id()) =&gt; {float(), float()}
}
```

Positions nodes in parallel layers (columns or rows).

Requires a list of layers, where each layer is a list of node IDs.

## Options

  * `:align` - Layer alignment direction: `:vertical` or `:horizontal` (default: `:vertical`).
  * `:width` - Bounding width (default: `1.0`).
  * `:height` - Bounding height (default: `1.0`).
  * `:center` - Center of layout space (default: `{0.0, 0.0}`).

## Examples

    iex> graph = Yog.undirected() |> Yog.add_nodes_from([1, 2, 3])
    iex> pos = Yog.Layout.Multipartite.layout(graph, [[1], [2, 3]])
    iex> Map.keys(pos) |> Enum.sort()
    [1, 2, 3]

---

*Consult [api-reference.md](api-reference.md) for complete listing*