graph-model

A graph is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of paired vertices, whose elements are called edges (sometimes links or lines).

For example we have V={1, 2, 3}

• E = [(1,2), (3,1]]
• graph G = (V, E)

Simple graph do not have multiple edges and loops and graph is undirected graph.

• multiple edges means graph E can be [(1,2), (1, 2), (3, 1)]
• graph has loops means graph can have E = [(1, 1), (1, 2), (3, 1)].
• graph is directed means edge (1, 2) and (2, 1) are different edges
• weighted graph means for every edge is assigned number(weight)

For this homework we will consider that graph is simple undirected weighted graph.

More information: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)

Implement Graph module as following:

1. Consider graph's vertices as Nodes and create class Note which will indicate graph's vertices

2. Graph class should has attributes

   • Edge dict
   • Vertex dict
   • Neighbours dict

   for example graph G in the begining of file - Edges = {(1, 2) : 2, (3, 1): 4}, where 2 and for are weights of (1, 2), (3, 1) edges - Vertives = {1, Node(1), 2: Node(2), 3: Node(3)} - Neighbours = {1: {2, 3}, 2: {1}, 3: {1}}

3. has method add_vertex(self, i) ---- creates Node for vertex if vertex doesn't exist in vertex list of Graph, and add neighbour set in Neighbours dict

4. has method delete_vertex(self, i) ---- deletes vertex from Vertex dict, delete edges of that vertex and delete neighbours and delete from neighbours list from Neighbours dict

5. has method add_edge(self, i, j, weight=None) ----- adds edge with vertices i, j, and assigns weight if Graph is weighted, and updates List, Neighbours dicts for i, j vertices and (i, j) line. If some of vertices doesn't exists creates one.

6. has __contains__(self, graph_2) method graph_2 in graph_1 or graph_1.__contains__(graph_2) should check if nodes of graph_2 contains in nodes of graph_1 and edges of graph_2 contains in edges of graph_1