Add and Remove vertex in Adjacency List representation of Graph

Prerequisites: Linked List, Graph Data Structure

In this article, adding and removing a vertex is discussed in a given adjacency list representation.

The graph can be represented in the Adjacency List representation as:

It is a Linked List representation where the head of the linked list is a vertex in the graph and all the connected nodes are the vertices to which the first vertex is connected. For example, from the graph, it is clear that vertex 0 is connected to vertex 4, 3 and 1. The same is representated in the adjacency list(or Linked List) representation.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

Adding a Vertex in the Graph: To add a vertex in the graph, the adjacency list can be iterated to the place where the insertion is required and the new node can be created using linked list implementation. For example, if 5 needs to be added between vertex 2 and vertex 3 such that vertex 3 points to vertex 5 and vertex 5 points to vertex 2, then a new edge is created between vertex 5 and vertex 3 and a new edge is created from vertex 5 and vertex 2. After adding the vertex, the adjacency list changes to:

Removing a Vertex in the Graph: To delete a vertex in the graph, iterate through the list of each vertex if an edge is present or not. If the edge is present, then delete the vertex in the same way as delete is performed in a linked list. For example, the adjacency list translates to the below list if vertex 4 is deleted from the list:

Below is the implementation of the above approach:

# Python implementation of the above approach 
# Implementing Linked List representation 
class AdjNode(object): 
    def __init__(self, data): 
        self.vertex = data 
        self.next = None
  
# Adjacency List representation 
class AdjList(object): 
  
    def __init__(self, vertices): 
        self.v = vertices 
        self.graph =[None]*self.v 
  
# Function to add an edge from a source vertex  
# to a destination vertex 
    def addedge(self, source, destination): 
        node = AdjNode(destination) 
        node.next = self.graph 
        self.graph= node 
  
# Function to call the above function. 
    def addvertex(self, vk, source, destination): 
        graph.addedge(source, vk)  
        graph.addedge(vk, destination) 
  
# Function to print the graph 
    def print_graph(self): 
        for i in range(self.v): 
            print(i, end ="") 
            temp = self.graph[i] 
            while temp: 
               print("->", temp.vertex, end ="") 
               temp = temp.next
            print("\n") 
  
# Function to delete a vertex 
    def delvertex(self, k): 
  
# Iterating through all the vertices of the graph 
        for i in range(self.v): 
            temp = self.graph[i] 
            if i == k: 
                while temp: 
                    self.graph[i]= temp.next
                    temp = self.graph[i] 
                      
            # Delete the vertex  
            # using linked list concept         
            if temp: 
                if temp.vertex == k: 
                    self.graph[i]= temp.next
                    temp = None
            while temp: 
                if temp.vertex == k: 
                    break
                prev = temp 
                temp = temp.next
  
            if temp == None: 
                continue
  
            prev.next = temp.next
            temp = None
      
  
# Driver code 
if __name__ == "__main__": 
  
    V = 6
    graph = AdjList(V)  
    graph.addedge(0, 1) 
    graph.addedge(0, 3) 
    graph.addedge(0, 4) 
    graph.addedge(1, 2) 
    graph.addedge(3, 2) 
    graph.addedge(4, 3) 
  
print("Initial adjacency list") 
graph.print_graph()  
  
# Add vertex 
graph.addvertex(5, 3, 2) 
print("Adjacency list after adding vertex") 
graph.print_graph()  
  
# Delete vertex 
graph.delvertex(4) 
print("Adjacency list after deleting vertex") 
graph.print_graph() 

Output:

Initial adjacency list
0-> 4-> 3-> 1

1-> 2

2

3-> 2

4-> 3

5

Adjacency list after adding vertex
0-> 4-> 3-> 1

1-> 2

2

3-> 5-> 2

4-> 3

5-> 2

Adjacency list after deleting vertex
0-> 3-> 1

1-> 2

2

3-> 5-> 2

4

5-> 2

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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