There are 2 popular ways of representing an undirected graph.

**Adjacency List**

Each list describes the set of neighbors of a vertex in the graph.

**Adjacency Matrix**

The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph.

Here’s an implementation of the above in Python:

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class Vertex: | |

def __init__(self, vertex): | |

self.name = vertex | |

self.neighbors = [] | |

def add_neighbor(self, neighbor): | |

if isinstance(neighbor, Vertex): | |

if neighbor.name not in self.neighbors: | |

self.neighbors.append(neighbor.name) | |

neighbor.neighbors.append(self.name) | |

self.neighbors = sorted(self.neighbors) | |

neighbor.neighbors = sorted(neighbor.neighbors) | |

else: | |

return False | |

def add_neighbors(self, neighbors): | |

for neighbor in neighbors: | |

if isinstance(neighbor, Vertex): | |

if neighbor.name not in self.neighbors: | |

self.neighbors.append(neighbor.name) | |

neighbor.neighbors.append(self.name) | |

self.neighbors = sorted(self.neighbors) | |

neighbor.neighbors = sorted(neighbor.neighbors) | |

else: | |

return False | |

def __repr__(self): | |

return str(self.neighbors) | |

class Graph: | |

def __init__(self): | |

self.vertices = {} | |

def add_vertex(self, vertex): | |

if isinstance(vertex, Vertex): | |

self.vertices[vertex.name] = vertex.neighbors | |

def add_vertices(self, vertices): | |

for vertex in vertices: | |

if isinstance(vertex, Vertex): | |

self.vertices[vertex.name] = vertex.neighbors | |

def add_edge(self, vertex_from, vertex_to): | |

if isinstance(vertex_from, Vertex) and isinstance(vertex_to, Vertex): | |

vertex_from.add_neighbor(vertex_to) | |

if isinstance(vertex_from, Vertex) and isinstance(vertex_to, Vertex): | |

self.vertices[vertex_from.name] = vertex_from.neighbors | |

self.vertices[vertex_to.name] = vertex_to.neighbors | |

def add_edges(self, edges): | |

for edge in edges: | |

self.add_edge(edge[0],edge[1]) | |

def adjacencyList(self): | |

if len(self.vertices) >= 1: | |

return [str(key) + ":" + str(self.vertices[key]) for key in self.vertices.keys()] | |

else: | |

return dict() | |

def adjacencyMatrix(self): | |

if len(self.vertices) >= 1: | |

self.vertex_names = sorted(g.vertices.keys()) | |

self.vertex_indices = dict(zip(self.vertex_names, range(len(self.vertex_names)))) | |

import numpy as np | |

self.adjacency_matrix = np.zeros(shape=(len(self.vertices),len(self.vertices))) | |

for i in range(len(self.vertex_names)): | |

for j in range(i, len(self.vertices)): | |

for el in g.vertices[self.vertex_names[i]]: | |

j = g.vertex_indices[el] | |

self.adjacency_matrix[i,j] = 1 | |

return self.adjacency_matrix | |

else: | |

return dict() | |

def graph(g): | |

""" Function to print a graph as adjacency list and adjacency matrix. """ | |

return str(g.adjacencyList()) + '\n' + '\n' + str(g.adjacencyMatrix()) | |

################################################################################### | |

a = Vertex('A') | |

b = Vertex('B') | |

c = Vertex('C') | |

d = Vertex('D') | |

e = Vertex('E') | |

a.add_neighbors([b,c,e]) | |

b.add_neighbors([a,c]) | |

c.add_neighbors([b,d,a,e]) | |

d.add_neighbor(c) | |

e.add_neighbors([a,c]) | |

g = Graph() | |

print(graph(g)) | |

print() | |

g.add_vertices([a,b,c,d,e]) | |

g.add_edge(b,d) | |

print(graph(g)) |

**Output:**

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{} | |

{} | |

["A:['B', 'C', 'E']", "C:['A', 'B', 'D', 'E']", "B:['A', 'C', 'D']", "E:['A', 'C']", "D:['B', 'C']"] | |

[[ 0. 1. 1. 0. 1.] | |

[ 1. 0. 1. 1. 0.] | |

[ 1. 1. 0. 1. 1.] | |

[ 0. 1. 1. 0. 0.] | |

[ 1. 0. 1. 0. 0.]] |