# `Yog.Connectivity.Analysis`
[🔗](https://github.com/code-shoily/yog_ex/blob/v0.97.0/lib/yog/connectivity/analysis.ex#L1)

Algorithms for analyzing graph connectivity (bridges, articulation points).

## Connectivity Analysis Visualization

**Articulation Points** (nodes) and **Bridges** (edges) are critical structural elements whose removal increases the number of connected components in the graph.

<div class="graphviz">
graph G {
  bgcolor="transparent";
  node [shape=circle, fontname="inherit"];
  edge [fontname="inherit", fontsize=10];

  // Articulation Points highlighted in rose
  3 [label="3", color="#f43f5e", penwidth=2.5, style=bold];
  4 [label="4", color="#f43f5e", penwidth=2.5, style=bold];
  
  // Group A
  1 -- 2; 2 -- 3; 3 -- 1;
  
  // Bridge (3 -- 4) highlighted in rose
  3 -- 4 [label="bridge", color="#f43f5e", penwidth=2.5, style=bold];
  
  // Group B
  4 -- 5; 5 -- 6; 6 -- 4;
}
</div>

    iex> alias Yog.Connectivity.Analysis
    iex> graph = Yog.from_edges(:undirected, [
    ...>   {1, 2, 1}, {2, 3, 1}, {3, 1, 1},
    ...>   {3, 4, 1},
    ...>   {4, 5, 1}, {5, 6, 1}, {6, 4, 1}
    ...> ])
    iex> result = Analysis.analyze(graph)
    iex> result.articulation_points
    [3, 4]
    iex> result.bridges
    [{3, 4}]

# `bridge`

```elixir
@type bridge() :: {Yog.node_id(), Yog.node_id()}
```

# `connectivity_results`

```elixir
@type connectivity_results() :: %{
  bridges: [bridge()],
  articulation_points: [Yog.node_id()]
}
```

# `analyze`

```elixir
@spec analyze(keyword() | Yog.graph()) :: connectivity_results()
```

Analyzes an **undirected graph** to find all bridges and articulation points.

---

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