Prerequisites: Graph and Its Representation
In this article, adding and removing edge is discussed in a given adjacency list representation.
A vector has been used to implement the graph using adjacency list representation. It is used to store the adjacency lists of all the vertices. The vertex number is used as the index in this vector.
Below is a graph and its adjacency list representation:
If the edge between 1 and 4 has to be removed, then the above graph and the adjacency list transforms to:
Approach: The idea is to represent the graph as an array of vectors such that every vector represents adjacency list of the vertex.
- Adding an edge: Adding an edge is done by inserting both of the vertices connected by that edge in each others list. For example, if an edge between (u, v) has to be added, then u is stored in v’s vector list and v is stored in u’s vector list. (push_back)
- Deleting an edge: To delete edge between (u, v), u’s adjacency list is traversed until v is found and it is removed from it. The same operation is performed for v.(erase)
Below is the implementation of the approach:
vertex 0 -> 1-> 4 vertex 1 -> 0-> 2-> 3-> 4 vertex 2 -> 1-> 3 vertex 3 -> 1-> 2-> 4 vertex 4 -> 0-> 1-> 3 vertex 0 -> 1-> 4 vertex 1 -> 0-> 2-> 3 vertex 2 -> 1-> 3 vertex 3 -> 1-> 2-> 4 vertex 4 -> 0-> 3
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- Convert Adjacency Matrix to Adjacency List representation of Graph
- Add and Remove vertex in Adjacency Matrix representation of Graph
- Prim’s MST for Adjacency List Representation | Greedy Algo-6
- Dijkstra’s Algorithm for Adjacency List Representation | Greedy Algo-8
- DFS for a n-ary tree (acyclic graph) represented as adjacency list
- Prim's Algorithm (Simple Implementation for Adjacency Matrix Representation)
- C program to implement Adjacency Matrix of a given Graph
- Edge Coloring of a Graph
- Check if removing a given edge disconnects a graph
- Program to Calculate the Edge Cover of a Graph
- Find weight of MST in a complete graph with edge-weights either 0 or 1
- Shortest Path in a weighted Graph where weight of an edge is 1 or 2
- Maximize number of nodes which are not part of any edge in a Graph
- Tree, Back, Edge and Cross Edges in DFS of Graph
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