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

Circular layout algorithm for positioning graph nodes in Elixir.

Positions nodes uniformly spaced along the circumference of a circle. This layout
highlights the cyclic structure of graphs and prevents node overlapping by design,
making it highly suitable for symmetric networks or cycle structures.

## Mathematical Model

Given a set of $N$ nodes, a circle centered at $(c_x, c_y)$ with radius $R$, the coordinates
for each node $i$ (where $0 \le i < N$) are calculated using polar coordinates:

$$\theta_i = \frac{2 \pi \cdot i}{N}$$
$$x_i = c_x + R \cdot \cos(\theta_i)$$
$$y_i = c_y + R \cdot \sin(\theta_i)$$

For a single-node graph ($N=1$), the node is positioned directly at the center $(c_x, c_y)$.

## Complexities

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

## References

* [Graphviz circular layout (circo) engine](https://graphviz.org/docs/layouts/)

# `layout`

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

Positions nodes uniformly spaced on a circle.

## Options

  * `:radius` - The radius of the circle (default: `1.0`).
  * `:center` - The `{x, y}` coordinates of the center of the circle (default: `{0.0, 0.0}`).

## Examples

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

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