dsa.graph API documentation
Description: Module containing graph classes.

# Module `dsa.graph`

Module containing graph classes.

## Classes

`class AdjacencyListGraph`

  A unweighted adjacency list vertex implementation (allows either directed or undirected representation) vertex labels are string types

  Expand source code

      class AdjacencyListGraph:
          """
          A unweighted adjacency list vertex implementation
          (allows either directed or undirected representation)
          vertex labels are string types
          """
          def __init__(self):
              #: hash table of vertices in graph
              self._adjacents = {}

          def add_edge(self, start_label: str, end_label: str, directed=False):
              """
              Add a vertex to the adjacency list.

              Args:
                  start_label (str): The label of the starting vertex.
                  end_label (str): The label of the ending vertex.
                  directed (bool): Whether the edge is directed.
              """
              self.add_directed_edge(start_label, end_label)
              self.add_directed_edge(end_label, start_label)

          def add_directed_edge(self, start_label: str, end_label: str):
              """
              Add a directed vertex to the adjacency list.

              Args:
                  start_label (str): The label of the starting vertex.
                  end_label (str): The label of the ending vertex.
              """
              if start_label not in self._adjacents:
                  self._adjacents[start_label] = [end_label]
              else:
                  if end_label not in self._adjacents[start_label]:
                      self._adjacents[start_label].append(end_label)
              if end_label not in self._adjacents:
                  self._adjacents[end_label] = []

          def delete_edge(self, start_label: str, end_label: str, directed=False):
              """
              Delete an undirected edge between two vertices.

              Args:
                  start_label (str): Starting vertex label.
                  end_label (str): Ending vertex label.
                  directed (bool): Whether the edge is directed.
              Raises:
                  KeyError: If the edge does exist.
              """
              if start_label not in self._adjacents:
                  raise KeyError(f"Vertex {start_label} does not exist")
              if end_label not in self._adjacents[start_label]:
                  raise KeyError(f"Vertex {end_label} does not exist")
              self._adjacents[start_label].remove(end_label)
              if not directed:
                  if end_label not in self._adjacents:
                      raise KeyError(f"Vertex {end_label} does not exist")
                  if start_label not in self._adjacents[end_label]:
                      raise KeyError(f"Vertex {start_label} does not exist")
                  self._adjacents[end_label].remove(start_label)

          def vertices(self) -> list:
              """
              Return a list of vertex labels of the graph
              """
              return list(self._adjacents.keys())

          def adjacents(self, vertex: str) -> list:
              """
              Return a list of adjacents of a given vertex

              Args:
                  vertex (str): The label of the vertex.
              """
              return self._adjacents[vertex]

          def df_traverse(self, start_label: str):
              """
              Return a list of vertices through depth first traversal starting at a given vertex.

              Args:
                  start_label (str): The starting vertex label.
              Returns:
                  A list of vertex labels.
              """
              return self._df_rec_traverse(start_label, set(), [])

          def _df_rec_traverse(self, start_label: str, visited, dflist):
              """
              Helper depth first traversal recursive function.
              """
              visited.add(start_label)
              dflist.append(start_label)

              for v in self[start_label]:
                  if v not in visited:
                      self._df_rec_traverse(v, visited, dflist)
              return dflist

          def bf_traverse(self, start_label: str):
              """
              Return a list of vertices through breadth first traversal starting at a given vertex
              Args:
                  start_label (str): The starting vertex label.
              Returns:
                  A list of vertex labels.
              """
              visited = set()
              q = Queue()
              bflist = []

              q.enqueue(start_label)
              visited.add(start_label)
              bflist.append(start_label)

              while len(q) > 0:
                  current = q.dequeue()

                  for v in self[current]:
                      if v not in visited:
                          visited.add(v)
                          q.enqueue(v)
                          bflist.append(v)
              return bflist

          def dfs(self, start_label:str, end_label:str) -> str:
              """
              Recursive depth first search.

              Args:
                  start_label (str): The starting vertex label.
                  end_label (str): The vertex label to search for.

              Returns:
                  A vertex in the graph if found, None otherwise.
              """
              def dfs_rec(current: str, end: str, visited):
                  if current == end:
                      return current

                  visited.add(current)

                  for v in self.adjacents(current):
                      if v not in visited:
                          result = dfs_rec(v, end, visited)
                          if result is not None:
                              return result

                  return None

              return dfs_rec(start_label, end_label, set())

          def bfs(self, start_label: str, end_label: str) -> str:
              """
              Breadth first search.

              Args:
                  start_label (str): The starting vertex label.
                  end_label (str): The vertex label to search for.

              Returns:
                  A vertex in the graph if found, None otherwise.
              """
              visited = set()
              queue = Queue()

              visited.add(start_label)
              queue.enqueue(start_label)

              while len(queue) > 0:
                  current = queue.dequeue()

                  if current == end_label:
                      return current

                  for v in self[current]:
                      if v not in visited:
                          visited.add(v)
                          queue.enqueue(v)

              return None

          def __getitem__(self, label: str):
              """
              Args:
                  vertex: vertex label
              Returns:
                  a list of adjacent vertex labels
              """

              return self._adjacents[label]

          def is_edge(self, start_label: str, end_label: str) -> bool:
              """
              Return boolean if an edge exists
              Args:
                  start_label (str): The starting vertex label.
                  end_label (str): The ending vertex label.

              Returns:
                  A boolean of whether there is an edge from start to end
              """
              return end_label in self[start_label]

          def __len__(self):
              return len(self._adjacents)

          def edges(self) -> list:
              """
              Return a list of edges in the graph. Each edge is represented by a tuple (start, end)
              """
              edges = []
              for start in self._adjacents.keys():
                  for end in self.adjacents(start):
                      if start != end:
                          edges.append((start, end))
              return edges

          def undirected_edges(self) -> list:
              """
              Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end)
              """
              edges = []
              for start in self._adjacents.keys():
                  for end in self.adjacents(start):
                      if start != end and (end, start) not in edges:
                          edges.append((start, end))
              return edges

  ### Subclasses

  - AdjacencyListWeightedGraph

  ### Methods

  `def add_directed_edge(self, start_label: str, end_label: str)`

    Add a directed vertex to the adjacency list.

    ## Args

    `start_label` :`str`
      The label of the starting vertex.
    `end_label` :`str`
      The label of the ending vertex.
  `def add_edge(self, start_label: str, end_label: str, directed=False)`

    Add a vertex to the adjacency list.

    ## Args

    `start_label` :`str`
      The label of the starting vertex.
    `end_label` :`str`
      The label of the ending vertex.
    `directed` :`bool`
      Whether the edge is directed.
  `def adjacents(self, vertex: str) ‑> list`

    Return a list of adjacents of a given vertex

    ## Args

    `vertex` :`str`
      The label of the vertex.
  `def bf_traverse(self, start_label: str)`

    Return a list of vertices through breadth first traversal starting at a given vertex

    ## Args

    `start_label` :`str`
      The starting vertex label.

    ## Returns

    A list of vertex labels.

  `def bfs(self, start_label: str, end_label: str) ‑> str`

    Breadth first search.

    ## Args

    `start_label` :`str`
      The starting vertex label.
    `end_label` :`str`
      The vertex label to search for.

    ## Returns

    A vertex in the graph if found, None otherwise.

  `def delete_edge(self, start_label: str, end_label: str, directed=False)`

    Delete an undirected edge between two vertices.

    ## Args

    `start_label` :`str`
      Starting vertex label.
    `end_label` :`str`
      Ending vertex label.
    `directed` :`bool`
      Whether the edge is directed.

    ## Raises

    `KeyError`
      If the edge does exist.
  `def df_traverse(self, start_label: str)`

    Return a list of vertices through depth first traversal starting at a given vertex.

    ## Args

    `start_label` :`str`
      The starting vertex label.

    ## Returns

    A list of vertex labels.

  `def dfs(self, start_label: str, end_label: str) ‑> str`

    Recursive depth first search.

    ## Args

    `start_label` :`str`
      The starting vertex label.
    `end_label` :`str`
      The vertex label to search for.

    ## Returns

    A vertex in the graph if found, None otherwise.

  `def edges(self) ‑> list`

    Return a list of edges in the graph. Each edge is represented by a tuple (start, end)

  `def is_edge(self, start_label: str, end_label: str) ‑> bool`

    Return boolean if an edge exists

    ## Args

    `start_label` :`str`
      The starting vertex label.
    `end_label` :`str`
      The ending vertex label.

    ## Returns

    A boolean of whether there is an edge from start to end

  `def undirected_edges(self) ‑> list`

    Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end)

  `def vertices(self) ‑> list`

    Return a list of vertex labels of the graph

`class AdjacencyListWeightedGraph`

  A weighted adjacency list vertex implementation in Python (allows either directed or undirected representation)

  Expand source code

      class AdjacencyListWeightedGraph(AdjacencyListGraph):
          """
          A weighted adjacency list vertex implementation in Python
          (allows either directed or undirected representation)
          """
          def __init__(self):
              #: hash table of vertices in graph
              self._adjacents = {}

          def add_edge(self, start_label: str, end_label: str, weight, directed=False):
              """
              Add an edge to the graph.

              Args:
                  start_label: The starting vertex label.
                  end_label: The ending vertex label.
                  weight: The edge weight.
                  directed: Whether the edge is directed.
              """
              if start_label not in self._adjacents:
                  self._adjacents[start_label] = {}

              self._adjacents[start_label][end_label] = weight

              if not directed:
                  if end_label not in self._adjacents:
                      self._adjacents[end_label] = {}
                  self._adjacents[end_label][start_label] = weight

          def delete_edge(self, start_label: str, end_label: str, directed=False):
              """
              Delete an undirected edge between two vertices.

              Args:
                  start_label (str): Starting vertex label.
                  end_label (str): Ending vertex label.
                  directed (bool): Whether the edge is directed.

              Raises:
                  KeyError: If the edge does exist.
              """
              if start_label not in self._adjacents:
                  raise KeyError(f"Vertex {start_label} does not exist")
              if end_label not in self._adjacents[start_label]:
                  raise KeyError(f"Vertex {end_label} does not exist")
              del self._adjacents[start_label][end_label]
              if not directed:
                  if end_label not in self._adjacents:
                      raise KeyError(f"Vertex {end_label} does not exist")
                  if start_label not in self._adjacents[end_label]:
                      raise KeyError(f"Vertex {start_label} does not exist")
                  del self._adjacents[end_label][start_label]

          def adjacents(self, vertex: str) -> list:
              """
              Return a list of adjacents of a given vertex
              Args:
                  vertex: starting vertex label
              """
              return self._adjacents[vertex]

          def df_traverse(self):
              """
              Perform depth first traversal.
              """
              return self._df_traverse_rec(self, set())

          def _df_traverse_rec(self, vertex, visited=None):
              """
              helper depth first traversal recursive function
              """
              visited.add(vertex)

              for v in vertex.adjacents:
                  if v not in visited:
                      v._df_traverse_rec(v, visited)

          def bf_traverse(self):
              """
              Perform breadth first traversal.
              """
              start = self
              visited = set()
              queue = Queue()

              queue.enqueue(start)

              while len(queue) > 0:
                  current = queue.dequeue()

                  if current not in visited:
                      visited.add(current)

                      for v in current.adjacents:
                          queue.enqueue(v)

          def dfs(self, start_label: str, end_label: str) -> str:
              """
              Recursive depth first search.

              Args:
                  start_label: The starting vertex label.
                  end_label: The vertex label to search for.
              Returns:
                  vertex in the graph
                  none if not found.
              """
              return self.dfs_rec(start_label, end_label, set())

          def dfs_rec(self, current, end_label, visited=None):
              """
              Helper depth-first search recursive function.

              Args:
                  current: Current vertex
                  end_label: Target vertex label
                  visited: Set of visited vertices

              Returns:
                  vertex in the graph if found, None otherwise.
              """
              if visited is None:
                  visited = set()

              if current == end_label:
                  return current

              visited.add(current)

              for v in self.adjacents(current):
                  if v not in visited:
                      result = self.dfs_rec(v, end_label, visited)
                      if result is not None:
                          return result

              return None

          def bfs(self, start_label: str, end_label: str) -> str:
              """
              Recursive breadth first search.

              Args:
                  end: vertex to search for

              Returns:
                  vertex in the graph
                  None if not found.
              """
              visited = set()
              queue = Queue()

              visited.add(start_label)
              queue.enqueue(start_label)

              while not queue.is_empty():
                  current = queue.dequeue()

                  if current == end_label:
                      return current

                  for v in self[current]:
                      if v not in visited:
                          visited.add(v)
                          queue.enqueue(v)

              return None

          def __getitem__(self, vertex: str) -> dict:
              """
              Args:
                  vertex: vertex label
              Returns:
              Return a hashtable of adjacent vertices
              """
              if vertex not in self._adjacents:
                  return {}
              return self._adjacents[vertex]

          def __len__(self):
              return len(self._adjacents)

          def edges(self) -> list:
              """
              Return a list of edges in the graph. Each edge is represented by a tuple (start, end, weight)
              """
              edges = []
              for start in self._adjacents.keys():
                  for end in self.adjacents(start):
                      weight = self[start][end]
                      if start != end:
                          edges.append((start, end, weight))
              return edges

          def undirected_edges(self) -> list:
              """
              Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end, weight)
              """
              edges = []
              for start in self._adjacents.keys():
                  for end in self.adjacents(start):
                      weight = self[start][end]
                      if start != end and (end, start, weight) not in edges:
                          edges.append((start, end, weight))
              return edges

          def is_edge(self, start_label: str, end_label: str) -> bool:
              """
              Return boolean if an edge exists
              Args:
                  start_label (str): starting vertex label
                  end_label (str): starting vertex label

              Returns:
                  A boolean of whether there is an edge from start to end.
              """
              return end_label in self[start_label]

  ### Ancestors

  - AdjacencyListGraph

  ### Methods

  `def add_edge(self, start_label: str, end_label: str, weight, directed=False)`

    Add an edge to the graph.

    ## Args

    `start_label`
      The starting vertex label.
    `end_label`
      The ending vertex label.
    `weight`
      The edge weight.
    `directed`
      Whether the edge is directed.
  `def adjacents(self, vertex: str) ‑> list`

    Return a list of adjacents of a given vertex

    ## Args

    `vertex`
      starting vertex label
  `def bf_traverse(self)`

    Perform breadth first traversal.

  `def bfs(self, start_label: str, end_label: str) ‑> str`

    Recursive breadth first search.

    ## Args

    `end`
      vertex to search for

    ## Returns

    vertex in the graph None if not found.

  `def delete_edge(self, start_label: str, end_label: str, directed=False)`

    Delete an undirected edge between two vertices.

    ## Args

    `start_label` :`str`
      Starting vertex label.
    `end_label` :`str`
      Ending vertex label.
    `directed` :`bool`
      Whether the edge is directed.

    ## Raises

    `KeyError`
      If the edge does exist.
  `def df_traverse(self)`

    Perform depth first traversal.

  `def dfs(self, start_label: str, end_label: str) ‑> str`

    Recursive depth first search.

    ## Args

    `start_label`
      The starting vertex label.
    `end_label`
      The vertex label to search for.

    ## Returns

    vertex in the graph none if not found.

  `def dfs_rec(self, current, end_label, visited=None)`

    Helper depth-first search recursive function.

    ## Args

    `current`
      Current vertex
    `end_label`
      Target vertex label
    `visited`
      Set of visited vertices

    ## Returns

    vertex in the graph if found, None otherwise.

  `def edges(self) ‑> list`

    Return a list of edges in the graph. Each edge is represented by a tuple (start, end, weight)

  `def is_edge(self, start_label: str, end_label: str) ‑> bool`

    Return boolean if an edge exists

    ## Args

    `start_label` :`str`
      starting vertex label
    `end_label` :`str`
      starting vertex label

    ## Returns

    A boolean of whether there is an edge from start to end.

  `def undirected_edges(self) ‑> list`

    Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end, weight)

  ### Inherited members

  - `AdjacencyListGraph`:
    - `add_directed_edge`
    - `vertices`
`class AdjacencyMatrixGraph (labels: list[str])`

  An unweighted adjacency matrix graph implementation.

  This class allows either directed or undirected representation of a graph. Vertex labels are string types.

  Initialize the graph with a list of vertex labels.

  ## Args

  `labels` :`list[str]`
    List of labels for each vertex.
  Expand source code

      class AdjacencyMatrixGraph:
          """
          An unweighted adjacency matrix graph implementation.

          This class allows either directed or undirected representation of a graph.
          Vertex labels are string types.
          """
          def __init__(self, labels: list[str]):
              """
              Initialize the graph with a list of vertex labels.

              Args:
                  labels (list[str]): List of labels for each vertex.
              """
              self.labels = labels
              self.label_index = { label: index for index, label  in enumerate(labels) }

              node_count = len(self.labels)
              self.array = [[None for i in range(node_count)] for j in range(node_count)]

          def add_edge(self, start_label: str, end_label: str, directed=False):
              """
              Add an edge between two vertices.

              Args:
                  start_label (str): Starting vertex label.
                  end_label (str): Ending vertex label.
                  directed (bool): Whether the edge is directed.
              """
              a = self.label_index[start_label]
              b = self.label_index[end_label]
              self.array[a][b] = True
              if not directed:
                  self.array[b][a] = True

          def add_vertex(self, label: str):
              """
              Add a vertex to the graph.

              Args:
                  label (str): The vertex label to add.
              """
              self.labels.append(label)
              self.label_index[label] = len(self.labels) - 1
              for row in self.array:
                  row.append(None)
              self.array.append([None for i in range(len(self.labels))])

          def delete_vertex(self, label: str):
              """
              Delete a vertex from the graph.

              Args:
                  label (str): The vertex label to delete.
              """
              index = self.label_index[label]
              self.labels.pop(index)
              self.label_index = { label: index for index, label in enumerate(self.labels) }
              self.array.pop(index)
              for row in self.array:
                  row.pop(index)

          def delete_edge(self, start_label: str, end_label: str, directed=False):
              """
              Delete an edge between two vertices.

              Args:
                  start_label (str): Starting vertex label.
                  end_label (str): Ending vertex label.
                  directed (bool): Whether the edge is directed.
              """
              a = self.label_index[start_label]
              b = self.label_index[end_label]
              if self.array[a][b] is None:
                  raise KeyError(f"Edge {start_label} to {end_label} does not exist")

              self.array[a][b] = None
              if not directed:
                  if self.array[b][a] is None:
                      raise KeyError(f"Edge {end_label} to {start_label} does not exist")
                  self.array[b][a] = None

          def df_traverse(self, start_label: str):
              """
              Perform depth first traversal in an adjacency matrix

              Args:
                  start_label (str): Starting vertex label.

              Returns:
                  Array with depth first order traversal.
              """
              return self._df_rec_traverse(start_label, set(), [])

          def _df_rec_traverse(self, start_label: str, visited, dfs):
              """
              Helper method for depth first recursive traversal
              """
              start_index = self.label_index[start_label]
              visited.add(start_label)
              dfs.append(self.labels[start_index])

              for adj_index, is_connected in enumerate(self.array[start_index]):
                  adj_label = self.labels[adj_index]
                  if is_connected and adj_label not in visited:
                      self._df_rec_traverse(adj_label, visited, dfs)

              return dfs

          def bf_traverse(self, start_label: str):
              """
              Perform breadth first traversal in an adjacency matrix.

              Args:
                  start_label (str): Starting vertex label.

              Returns:
                  Array with breadth first order traversal.
              """
              bfs = []
              q = Queue()
              visited = set()

              start_index = self.label_index[start_label]
              q.enqueue(start_index)
              bfs.append(self.labels[start_index])
              while not q.is_empty():
                  current = q.dequeue()
                  for i in range(len(self.array)):
                      if start_index != i and self.array[current][i] and (i not in visited):
                          visited.add(i)
                          q.enqueue(i)
                          bfs.append(self.labels[i])
              return bfs

          def vertices(self) -> list:
              """
              Return a list of vertex labels of the graph
              """
              return self.labels

          def edges(self) -> list:
              """
              Return a list of edges in the graph. Each edge is represented by a tuple (start, end)
              """
              edges = []
              vertex_count = len(self.labels)
              for i in range(vertex_count):
                  for j in range(vertex_count):
                      if self.array[i][j] and i != j:
                          edges.append((self.labels[i], self.labels[j]))

              return edges

          def undirected_edges(self) -> list:
              """
              Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end)
              """
              edges = []
              vertex_count = len(self.labels)
              for i in range(vertex_count):
                  for j in range(vertex_count):
                      if self.array[i][j] and i != j and (self.labels[j], self.labels[i]) not in edges:
                          edges.append((self.labels[i], self.labels[j]))

              return edges

          def is_edge(self, start_label: str, end_label: str) -> bool:
              """
              Return boolean if an edge exists.

              Args:
                  start_label (str): starting vertex label
                  end_label (str): starting vertex label

              Returns:0
                  A boolean of whether there is an edge from start to end.
              """
              start_index = self.label_index[start_label]
              end_index = self.label_index[end_label]

              return self.array[start_index][end_index] is not None

          def __getitem__(self, vertex: str) -> list:
              """
              Args:
                  vertex (str): The vertex label.
              Returns:
                  A list of adjacent vertex labels.
              """
              index = self.label_index[vertex]
              return [self.labels[i] for i in range(len(self.array[index])) if self.array[index][i]]

          def print_graph(self):
              """
              Print the contents of the graph.
              """
              print("   |", end="")
              for label in self.labels:
                  print(f"{label:^3}", end=" ")
              print()
              print("----" * (len(self.array) + 1))
              for r, row in enumerate(self.array):
                  label = self.labels[r]
                  print(f"{label:^3}|", end="")
                  for col in row:
                      b = " T " if col else "   "
                      print(b, end=" ")
                  print()

  ### Subclasses

  - AdjacencyMatrixWeightedGraph

  ### Methods

  `def add_edge(self, start_label: str, end_label: str, directed=False)`

    Add an edge between two vertices.

    ## Args

    `start_label` :`str`
      Starting vertex label.
    `end_label` :`str`
      Ending vertex label.
    `directed` :`bool`
      Whether the edge is directed.
  `def add_vertex(self, label: str)`

    Add a vertex to the graph.

    ## Args

    `label` :`str`
      The vertex label to add.
  `def bf_traverse(self, start_label: str)`

    Perform breadth first traversal in an adjacency matrix.

    ## Args

    `start_label` :`str`
      Starting vertex label.

    ## Returns

    Array with breadth first order traversal.

  `def delete_edge(self, start_label: str, end_label: str, directed=False)`

    Delete an edge between two vertices.

    ## Args

    `start_label` :`str`
      Starting vertex label.
    `end_label` :`str`
      Ending vertex label.
    `directed` :`bool`
      Whether the edge is directed.
  `def delete_vertex(self, label: str)`

    Delete a vertex from the graph.

    ## Args

    `label` :`str`
      The vertex label to delete.
  `def df_traverse(self, start_label: str)`

    Perform depth first traversal in an adjacency matrix

    ## Args

    `start_label` :`str`
      Starting vertex label.

    ## Returns

    Array with depth first order traversal.

  `def edges(self) ‑> list`

    Return a list of edges in the graph. Each edge is represented by a tuple (start, end)

  `def is_edge(self, start_label: str, end_label: str) ‑> bool`

    Return boolean if an edge exists.

    ## Args

    `start_label` :`str`
      starting vertex label
    `end_label` :`str`
      starting vertex label

    Returns:0 A boolean of whether there is an edge from start to end.

  `def print_graph(self)`

    Print the contents of the graph.

  `def undirected_edges(self) ‑> list`

    Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end)

  `def vertices(self) ‑> list`

    Return a list of vertex labels of the graph

`class AdjacencyMatrixWeightedGraph (labels)`

  A weighted adjacency matrix graph implementation (allows either directed or undirected representation) vertex labels are string types

  ## Args

  `labels`
    list of labels for each vertex (string types)
  Expand source code

      class AdjacencyMatrixWeightedGraph(AdjacencyMatrixGraph):
          """
          A weighted adjacency matrix graph implementation
          (allows either directed or undirected representation)
          vertex labels are string types
          """
          def __init__(self, labels):
              """
              Args:
                  labels: list of labels for each vertex (string types)
              """
              super().__init__(labels)

          def add_edge(self, start_label: str, end_label: str, weight, directed=False):
              """
              Add an undirected edge between one vertex to another

              Args:
                  start_label (str): The starting vertex label.
                  end_label (str): The ending vertex label.
                  weight: The weight of the vertex.
                  directed: Whether the edge is directed.
              """
              a = self.label_index[start_label]
              b = self.label_index[end_label]

              self.array[a][b] = weight
              self.array[a][a] = 0
              self.array[b][b] = 0

              if not directed:
                  self.array[b][a] = weight

          def print_graph(self):
              """
              Print the contents of the graph.
              """
              print("   |", end="")
              for label in self.labels:
                  print(f"{label:>3}", end=" ")
              print()
              print("----" * (len(self.array) + 1))
              for r, row in enumerate(self.array):
                  label = self.labels[r]
                  print(f"{label:^3}|", end="")
                  for col in row:
                      w = f"{col:3}" if col is not None else "   "
                      print(w, end=" ")
                  print()

          def edges(self) -> list:
              """
              Return a list of edges in the graph. Each edge is represented by a tuple (start, end, weight).
              """
              edges = []
              vertex_count = len(self.labels)
              for i in range(vertex_count):
                  for j in range(vertex_count):
                      weight = self.array[i][j]
                      if weight and i != j:
                          edges.append((self.labels[i], self.labels[j], weight))

              return edges

          def undirected_edges(self) -> list:
              """
              Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end, weight).
              """
              edges = []
              vertex_count = len(self.labels)
              for i in range(vertex_count):
                  for j in range(vertex_count):
                      weight = self.array[i][j]
                      if weight and i != j and (self.labels[j], self.labels[i], weight) not in edges:
                          edges.append((self.labels[i], self.labels[j], weight))

              return edges

          def is_edge(self, start_label: str, end_label: str) -> bool:
              """
              Return boolean if an edge exists.

              Args:
                  start_label (str): Starting vertex label.
                  end_label (str): Ending vertex label.

              Returns:
                  A boolean of whether there is an edge from start to end.
              """
              return super().is_edge(start_label, end_label)

          def weightx(self, start: str, end: str) -> bool:
              """
              Return weight of an edge (is this used???)
              Args:
                  start_label: starting vertex label
                  end_label: starting vertex label

              Returns:
                  weight value of an edge from start to end
              """
              return super().is_edge(start, end)

          def __getitem__(self, vertex: str) -> dict:
              """
              Args:
                  vertex: vertex label
              Returns:
                  a dictionary of adjacent vertex labels and weights
              """
              index = self.label_index[vertex]
              return {self.labels[i] : self.array[index][i] for i in range(len(self.array[index])) if self.array[index][i]}

  ### Ancestors

  - AdjacencyMatrixGraph

  ### Methods

  `def add_edge(self, start_label: str, end_label: str, weight, directed=False)`

    Add an undirected edge between one vertex to another

    ## Args

    `start_label` :`str`
      The starting vertex label.
    `end_label` :`str`
      The ending vertex label.
    `weight`
      The weight of the vertex.
    `directed`
      Whether the edge is directed.
  `def edges(self) ‑> list`

    Return a list of edges in the graph. Each edge is represented by a tuple (start, end, weight).

  `def is_edge(self, start_label: str, end_label: str) ‑> bool`

    Return boolean if an edge exists.

    ## Args

    `start_label` :`str`
      Starting vertex label.
    `end_label` :`str`
      Ending vertex label.

    ## Returns

    A boolean of whether there is an edge from start to end.

  `def undirected_edges(self) ‑> list`

    Return a list of undirected edges in the graph. Each edge is represented by a tuple (start, end, weight).

  `def weightx(self, start: str, end: str) ‑> bool`

    Return weight of an edge (is this used???)

    ## Args

    `start_label`
      starting vertex label
    `end_label`
      starting vertex label

    ## Returns

    weight value of an edge from start to end

  ### Inherited members

  - `AdjacencyMatrixGraph`:
    - `add_vertex`
    - `bf_traverse`
    - `delete_edge`
    - `delete_vertex`
    - `df_traverse`
    - `print_graph`
    - `vertices`