Graph Adjacency Matrix
n
#!/usr/bin/env python3
"""
Author: Vikram Nithyanandam
Description:
The following implementation is a robust unweighted Graph data structure
implemented using an adjacency matrix. This vertices and edges of this graph can be
effectively initialized and modified while storing your chosen generic
value in each vertex.
Adjacency Matrix: https://mathworld.wolfram.com/AdjacencyMatrix.html
Potential Future Ideas:
- Add a flag to set edge weights on and set edge weights
- Make edge weights and vertex values customizable to store whatever the client wants
- Support multigraph functionality if the client wants it
"""
from __future__ import annotations
import random
import unittest
from pprint import pformat
from typing import Generic, TypeVar
T = TypeVar("T")
class GraphAdjacencyMatrix(Generic[T]):
def __init__(
self, vertices: list[T], edges: list[list[T]], directed: bool = True
) -> None:
"""
Parameters:
- vertices: (list[T]) The list of vertex names the client wants to
pass in. Default is empty.
- edges: (list[list[T]]) The list of edges the client wants to
pass in. Each edge is a 2-element list. Default is empty.
- directed: (bool) Indicates if graph is directed or undirected.
Default is True.
"""
self.directed = directed
self.vertex_to_index: dict[T, int] = {}
self.adj_matrix: list[list[int]] = []
# Falsey checks
edges = edges or []
vertices = vertices or []
for vertex in vertices:
self.add_vertex(vertex)
for edge in edges:
if len(edge) != 2:
msg = f"Invalid input: {edge} must have length 2."
raise ValueError(msg)
self.add_edge(edge[0], edge[1])
def add_edge(self, source_vertex: T, destination_vertex: T) -> None:
"""
Creates an edge from source vertex to destination vertex. If any
given vertex doesn't exist or the edge already exists, a ValueError
will be thrown.
"""
if not (
self.contains_vertex(source_vertex)
and self.contains_vertex(destination_vertex)
):
msg = (
f"Incorrect input: Either {source_vertex} or "
f"{destination_vertex} does not exist"
)
raise ValueError(msg)
if self.contains_edge(source_vertex, destination_vertex):
msg = (
"Incorrect input: The edge already exists between "
f"{source_vertex} and {destination_vertex}"
)
raise ValueError(msg)
# Get the indices of the corresponding vertices and set their edge value to 1.
u: int = self.vertex_to_index[source_vertex]
v: int = self.vertex_to_index[destination_vertex]
self.adj_matrix[u][v] = 1
if not self.directed:
self.adj_matrix[v][u] = 1
def remove_edge(self, source_vertex: T, destination_vertex: T) -> None:
"""
Removes the edge between the two vertices. If any given vertex
doesn't exist or the edge does not exist, a ValueError will be thrown.
"""
if not (
self.contains_vertex(source_vertex)
and self.contains_vertex(destination_vertex)
):
msg = (
f"Incorrect input: Either {source_vertex} or "
f"{destination_vertex} does not exist"
)
raise ValueError(msg)
if not self.contains_edge(source_vertex, destination_vertex):
msg = (
"Incorrect input: The edge does NOT exist between "
f"{source_vertex} and {destination_vertex}"
)
raise ValueError(msg)
# Get the indices of the corresponding vertices and set their edge value to 0.
u: int = self.vertex_to_index[source_vertex]
v: int = self.vertex_to_index[destination_vertex]
self.adj_matrix[u][v] = 0
if not self.directed:
self.adj_matrix[v][u] = 0
def add_vertex(self, vertex: T) -> None:
"""
Adds a vertex to the graph. If the given vertex already exists,
a ValueError will be thrown.
"""
if self.contains_vertex(vertex):
msg = f"Incorrect input: {vertex} already exists in this graph."
raise ValueError(msg)
# build column for vertex
for row in self.adj_matrix:
row.append(0)
# build row for vertex and update other data structures
self.adj_matrix.append([0] * (len(self.adj_matrix) + 1))
self.vertex_to_index[vertex] = len(self.adj_matrix) - 1
def remove_vertex(self, vertex: T) -> None:
"""
Removes the given vertex from the graph and deletes all incoming and
outgoing edges from the given vertex as well. If the given vertex
does not exist, a ValueError will be thrown.
"""
if not self.contains_vertex(vertex):
msg = f"Incorrect input: {vertex} does not exist in this graph."
raise ValueError(msg)
# first slide up the rows by deleting the row corresponding to
# the vertex being deleted.
start_index = self.vertex_to_index[vertex]
self.adj_matrix.pop(start_index)
# next, slide the columns to the left by deleting the values in
# the column corresponding to the vertex being deleted
for lst in self.adj_matrix:
lst.pop(start_index)
# final clean up
self.vertex_to_index.pop(vertex)
# decrement indices for vertices shifted by the deleted vertex in the adj matrix
for vertex in self.vertex_to_index:
if self.vertex_to_index[vertex] >= start_index:
self.vertex_to_index[vertex] = self.vertex_to_index[vertex] - 1
def contains_vertex(self, vertex: T) -> bool:
"""
Returns True if the graph contains the vertex, False otherwise.
"""
return vertex in self.vertex_to_index
def contains_edge(self, source_vertex: T, destination_vertex: T) -> bool:
"""
Returns True if the graph contains the edge from the source_vertex to the
destination_vertex, False otherwise. If any given vertex doesn't exist, a
ValueError will be thrown.
"""
if not (
self.contains_vertex(source_vertex)
and self.contains_vertex(destination_vertex)
):
msg = (
f"Incorrect input: Either {source_vertex} "
f"or {destination_vertex} does not exist."
)
raise ValueError(msg)
u = self.vertex_to_index[source_vertex]
v = self.vertex_to_index[destination_vertex]
return self.adj_matrix[u][v] == 1
def clear_graph(self) -> None:
"""
Clears all vertices and edges.
"""
self.vertex_to_index = {}
self.adj_matrix = []
def __repr__(self) -> str:
first = "Adj Matrix:\n" + pformat(self.adj_matrix)
second = "\nVertex to index mapping:\n" + pformat(self.vertex_to_index)
return first + second
class TestGraphMatrix(unittest.TestCase):
def __assert_graph_edge_exists_check(
self,
undirected_graph: GraphAdjacencyMatrix,
directed_graph: GraphAdjacencyMatrix,
edge: list[int],
) -> None:
self.assertTrue(undirected_graph.contains_edge(edge[0], edge[1]))
self.assertTrue(undirected_graph.contains_edge(edge[1], edge[0]))
self.assertTrue(directed_graph.contains_edge(edge[0], edge[1]))
def __assert_graph_edge_does_not_exist_check(
self,
undirected_graph: GraphAdjacencyMatrix,
directed_graph: GraphAdjacencyMatrix,
edge: list[int],
) -> None:
self.assertFalse(undirected_graph.contains_edge(edge[0], edge[1]))
self.assertFalse(undirected_graph.contains_edge(edge[1], edge[0]))
self.assertFalse(directed_graph.contains_edge(edge[0], edge[1]))
def __assert_graph_vertex_exists_check(
self,
undirected_graph: GraphAdjacencyMatrix,
directed_graph: GraphAdjacencyMatrix,
vertex: int,
) -> None:
self.assertTrue(undirected_graph.contains_vertex(vertex))
self.assertTrue(directed_graph.contains_vertex(vertex))
def __assert_graph_vertex_does_not_exist_check(
self,
undirected_graph: GraphAdjacencyMatrix,
directed_graph: GraphAdjacencyMatrix,
vertex: int,
) -> None:
self.assertFalse(undirected_graph.contains_vertex(vertex))
self.assertFalse(directed_graph.contains_vertex(vertex))
def __generate_random_edges(
self, vertices: list[int], edge_pick_count: int
) -> list[list[int]]:
self.assertTrue(edge_pick_count <= len(vertices))
random_source_vertices: list[int] = random.sample(
vertices[0 : int(len(vertices) / 2)], edge_pick_count
)
random_destination_vertices: list[int] = random.sample(
vertices[int(len(vertices) / 2) :], edge_pick_count
)
random_edges: list[list[int]] = []
for source in random_source_vertices:
for dest in random_destination_vertices:
random_edges.append([source, dest])
return random_edges
def __generate_graphs(
self, vertex_count: int, min_val: int, max_val: int, edge_pick_count: int
) -> tuple[GraphAdjacencyMatrix, GraphAdjacencyMatrix, list[int], list[list[int]]]:
if max_val - min_val + 1 < vertex_count:
raise ValueError(
"Will result in duplicate vertices. Either increase "
"range between min_val and max_val or decrease vertex count"
)
# generate graph input
random_vertices: list[int] = random.sample(
range(min_val, max_val + 1), vertex_count
)
random_edges: list[list[int]] = self.__generate_random_edges(
random_vertices, edge_pick_count
)
# build graphs
undirected_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=random_edges, directed=False
)
directed_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=random_edges, directed=True
)
return undirected_graph, directed_graph, random_vertices, random_edges
def test_init_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
# test graph initialization with vertices and edges
for num in random_vertices:
self.__assert_graph_vertex_exists_check(
undirected_graph, directed_graph, num
)
for edge in random_edges:
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, edge
)
self.assertFalse(undirected_graph.directed)
self.assertTrue(directed_graph.directed)
def test_contains_vertex(self) -> None:
random_vertices: list[int] = random.sample(range(101), 20)
# Build graphs WITHOUT edges
undirected_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=False
)
directed_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=True
)
# Test contains_vertex
for num in range(101):
self.assertEqual(
num in random_vertices, undirected_graph.contains_vertex(num)
)
self.assertEqual(
num in random_vertices, directed_graph.contains_vertex(num)
)
def test_add_vertices(self) -> None:
random_vertices: list[int] = random.sample(range(101), 20)
# build empty graphs
undirected_graph: GraphAdjacencyMatrix = GraphAdjacencyMatrix(
vertices=[], edges=[], directed=False
)
directed_graph: GraphAdjacencyMatrix = GraphAdjacencyMatrix(
vertices=[], edges=[], directed=True
)
# run add_vertex
for num in random_vertices:
undirected_graph.add_vertex(num)
for num in random_vertices:
directed_graph.add_vertex(num)
# test add_vertex worked
for num in random_vertices:
self.__assert_graph_vertex_exists_check(
undirected_graph, directed_graph, num
)
def test_remove_vertices(self) -> None:
random_vertices: list[int] = random.sample(range(101), 20)
# build graphs WITHOUT edges
undirected_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=False
)
directed_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=True
)
# test remove_vertex worked
for num in random_vertices:
self.__assert_graph_vertex_exists_check(
undirected_graph, directed_graph, num
)
undirected_graph.remove_vertex(num)
directed_graph.remove_vertex(num)
self.__assert_graph_vertex_does_not_exist_check(
undirected_graph, directed_graph, num
)
def test_add_and_remove_vertices_repeatedly(self) -> None:
random_vertices1: list[int] = random.sample(range(51), 20)
random_vertices2: list[int] = random.sample(range(51, 101), 20)
# build graphs WITHOUT edges
undirected_graph = GraphAdjacencyMatrix(
vertices=random_vertices1, edges=[], directed=False
)
directed_graph = GraphAdjacencyMatrix(
vertices=random_vertices1, edges=[], directed=True
)
# test adding and removing vertices
for i, _ in enumerate(random_vertices1):
undirected_graph.add_vertex(random_vertices2[i])
directed_graph.add_vertex(random_vertices2[i])
self.__assert_graph_vertex_exists_check(
undirected_graph, directed_graph, random_vertices2[i]
)
undirected_graph.remove_vertex(random_vertices1[i])
directed_graph.remove_vertex(random_vertices1[i])
self.__assert_graph_vertex_does_not_exist_check(
undirected_graph, directed_graph, random_vertices1[i]
)
# remove all vertices
for i, _ in enumerate(random_vertices1):
undirected_graph.remove_vertex(random_vertices2[i])
directed_graph.remove_vertex(random_vertices2[i])
self.__assert_graph_vertex_does_not_exist_check(
undirected_graph, directed_graph, random_vertices2[i]
)
def test_contains_edge(self) -> None:
# generate graphs and graph input
vertex_count = 20
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(vertex_count, 0, 100, 4)
# generate all possible edges for testing
all_possible_edges: list[list[int]] = []
for i in range(vertex_count - 1):
for j in range(i + 1, vertex_count):
all_possible_edges.append([random_vertices[i], random_vertices[j]])
all_possible_edges.append([random_vertices[j], random_vertices[i]])
# test contains_edge function
for edge in all_possible_edges:
if edge in random_edges:
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, edge
)
elif [edge[1], edge[0]] in random_edges:
# since this edge exists for undirected but the reverse may
# not exist for directed
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, [edge[1], edge[0]]
)
else:
self.__assert_graph_edge_does_not_exist_check(
undirected_graph, directed_graph, edge
)
def test_add_edge(self) -> None:
# generate graph input
random_vertices: list[int] = random.sample(range(101), 15)
random_edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
# build graphs WITHOUT edges
undirected_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=False
)
directed_graph = GraphAdjacencyMatrix(
vertices=random_vertices, edges=[], directed=True
)
# run and test add_edge
for edge in random_edges:
undirected_graph.add_edge(edge[0], edge[1])
directed_graph.add_edge(edge[0], edge[1])
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, edge
)
def test_remove_edge(self) -> None:
# generate graph input and graphs
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
# run and test remove_edge
for edge in random_edges:
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, edge
)
undirected_graph.remove_edge(edge[0], edge[1])
directed_graph.remove_edge(edge[0], edge[1])
self.__assert_graph_edge_does_not_exist_check(
undirected_graph, directed_graph, edge
)
def test_add_and_remove_edges_repeatedly(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
# make some more edge options!
more_random_edges: list[list[int]] = []
while len(more_random_edges) != len(random_edges):
edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
for edge in edges:
if len(more_random_edges) == len(random_edges):
break
elif edge not in more_random_edges and edge not in random_edges:
more_random_edges.append(edge)
for i, _ in enumerate(random_edges):
undirected_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
directed_graph.add_edge(more_random_edges[i][0], more_random_edges[i][1])
self.__assert_graph_edge_exists_check(
undirected_graph, directed_graph, more_random_edges[i]
)
undirected_graph.remove_edge(random_edges[i][0], random_edges[i][1])
directed_graph.remove_edge(random_edges[i][0], random_edges[i][1])
self.__assert_graph_edge_does_not_exist_check(
undirected_graph, directed_graph, random_edges[i]
)
def test_add_vertex_exception_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
for vertex in random_vertices:
with self.assertRaises(ValueError):
undirected_graph.add_vertex(vertex)
with self.assertRaises(ValueError):
directed_graph.add_vertex(vertex)
def test_remove_vertex_exception_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
for i in range(101):
if i not in random_vertices:
with self.assertRaises(ValueError):
undirected_graph.remove_vertex(i)
with self.assertRaises(ValueError):
directed_graph.remove_vertex(i)
def test_add_edge_exception_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
for edge in random_edges:
with self.assertRaises(ValueError):
undirected_graph.add_edge(edge[0], edge[1])
with self.assertRaises(ValueError):
directed_graph.add_edge(edge[0], edge[1])
def test_remove_edge_exception_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
more_random_edges: list[list[int]] = []
while len(more_random_edges) != len(random_edges):
edges: list[list[int]] = self.__generate_random_edges(random_vertices, 4)
for edge in edges:
if len(more_random_edges) == len(random_edges):
break
elif edge not in more_random_edges and edge not in random_edges:
more_random_edges.append(edge)
for edge in more_random_edges:
with self.assertRaises(ValueError):
undirected_graph.remove_edge(edge[0], edge[1])
with self.assertRaises(ValueError):
directed_graph.remove_edge(edge[0], edge[1])
def test_contains_edge_exception_check(self) -> None:
(
undirected_graph,
directed_graph,
random_vertices,
random_edges,
) = self.__generate_graphs(20, 0, 100, 4)
for vertex in random_vertices:
with self.assertRaises(ValueError):
undirected_graph.contains_edge(vertex, 102)
with self.assertRaises(ValueError):
directed_graph.contains_edge(vertex, 102)
with self.assertRaises(ValueError):
undirected_graph.contains_edge(103, 102)
with self.assertRaises(ValueError):
directed_graph.contains_edge(103, 102)
if __name__ == "__main__":
unittest.main()
