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+# AOC 2024 Day 23
+
+## Section
+
+```elixir
+defmodule LANGraph do
+  defstruct nodes: MapSet.new, edges: MapSet.new
+  @doc """
+  For a graph, counts the number of cycles of size `size` in the graph.
+  """
+  def cycles(graph, 3) do
+    nodes = graph.nodes
+
+    nodes
+    |> Enum.flat_map(
+      fn v -> find_cycle(graph, v, v, [], 3, 0) end
+    )
+  end
+
+  def find_cycle(_, _, _, path, n, y) when y == n, do: [path]
+  def find_cycle(graph, start, v, path, depth, curr) do
+    is_next_node? = fn u -> 
+      if curr == (depth - 1), do: u == start, else: Enum.all?(path, &(&1 != u))
+    end
+  
+    outE(graph, v)
+    |> Stream.map(fn {uu, vv} -> if uu == v, do: vv, else: uu end)
+    |> Stream.filter(is_next_node?)
+    |> Enum.flat_map(&find_cycle(graph, start, &1, [v | path], depth, curr + 1))
+  end
+
+  defp outE(graph, vertex) do
+    graph.edges
+    |> Enum.filter(&(elem(&1,0) == vertex or elem(&1,1) == vertex))
+  end
+  
+  def add_edge(graph, {a, b} = edge) do
+    %LANGraph{
+      nodes: graph.nodes |> MapSet.put(a) |> MapSet.put(b),
+      edges: graph.edges |> MapSet.put(edge)
+    }
+  end
+
+  def neighbors(graph, vertex) do
+    graph.edges 
+    |> Stream.filter(&(elem(&1, 0) == vertex or elem(&1, 1) == vertex))
+    |> Enum.map(fn 
+      {^vertex, b} -> b 
+      {b, ^vertex} -> b
+    end)
+  end
+  
+  @empty MapSet.new([])
+  def bron_kerbosch(g) do
+    Process.delete(:maximal)
+    neighbor_set = fn v ->
+      n = neighbors(g, v)  |> MapSet.new()
+      n
+    end
+    bron_kerbosch(MapSet.new, g.nodes, MapSet.new, neighbor_set)
+  end
+  
+  def bron_kerbosch(r,o,o,_) when o == @empty do
+    Process.put(
+        :maximal,
+        case Process.get(:maximal) do
+          nil -> [r]
+          l -> [r | l]
+        end
+    )
+  end
+  def bron_kerbosch(_,o,_,_) when o == @empty, do: @empty
+  def bron_kerbosch(r,p,x,n) do
+    for v <- p,
+      n_v = n.(v),
+      reduce: {p, x} do
+      {p, x} -> 
+        bron_kerbosch(MapSet.put(r, v), MapSet.intersection(p, n_v), MapSet.intersection(x, n_v), n)
+        {p |> MapSet.delete(v), x |> MapSet.put(v)}
+    end
+  end
+
+  def parse(input), do: input 
+    |> String.split("\n", trim: true)
+    |> Stream.map(fn <<a::binary-size(2)>> <> "-" <> <<b::binary-size(2)>> ->
+      {a |> String.to_atom, b |> String.to_atom}
+    end)
+    |> Enum.reduce(%LANGraph{}, fn e, acc -> LANGraph.add_edge(acc, e) end)
+
+  def part1(input) do
+    connections = input |> parse()
+      
+    t_nodes = connections.nodes|> Stream.filter(&String.starts_with?(Atom.to_string(&1), "t")) |> Enum.into(MapSet.new)
+    three_cycles = connections 
+      |> LANGraph.cycles(3)
+      |> Enum.map(&Enum.into(&1, MapSet.new())) 
+      |> Enum.into(MapSet.new)
+    three_cycles
+      |> Stream.filter(&Enum.any?(t_nodes, fn t -> MapSet.member?(&1, t) end))
+      |> Enum.count()
+  end
+
+  def part2(input) do
+    input
+    |> parse() 
+    |> bron_kerbosch()
+    
+    Process.get(:maximal)
+    |> Enum.max_by(&MapSet.size/1)
+    |> Stream.map(&Atom.to_string/1)
+    |> Enum.sort 
+    |> Enum.join(",")
+  end
+end
+```
+
+## Input
+
+```elixir
+input = """
+"""
+
+connections = input |> String.split("\n", trim: true)
+|> Stream.map(fn <<a::binary-size(2)>> <> "-" <> <<b::binary-size(2)>> ->
+  {a |> String.to_atom, b |> String.to_atom}
+end)
+|> Enum.reduce(%LANGraph{}, fn e, acc -> LANGraph.add_edge(acc, e) end)
+
+```
+
+## Solution
+
+```elixir
+LANGraph.part1(input)
+```
+
+```elixir
+LANGraph.part2(input)
+```