What Is Multigraph in Data Structure?
When studying data structures, it is important to understand different types of graphs. One such type is a multigraph, which is a graph that allows multiple edges between two vertices and even loops where an edge connects a vertex to itself.
Definition:
A multigraph, also known as a pseudograph, is an extension of a simple graph. In a simple graph, each edge connects two distinct vertices, whereas in a multigraph, there can be multiple edges between the same pair of vertices.
Representation:
In order to represent a multigraph efficiently, we can use an adjacency list or an adjacency matrix. The choice depends on the specific requirements and operations performed on the multigraph.
Adjacency List Representation:
In the adjacency list representation of a multigraph, we maintain an array of lists. Each element in the array represents a vertex, and the corresponding list contains all the adjacent vertices connected by edges.
Here is an example of an adjacency list representation of a multigraph:
- List 0: 1 -> 2 -> 2 -> 3
- List 1: 0 -> 2 -> null
- List 2: 0 -> 0 -> 1
- List 3: 0
Adjacency Matrix Representation:
In the adjacency matrix representation of a multigraph, we use a two-dimensional matrix to represent the connections between vertices. The matrix element at index [i][j] represents the number of edges between vertex i and vertex j.
Here is an example of an adjacency matrix representation of a multigraph:
- 0 1 2 3
- 0 0 1 2 0
- 1 1 0 0 0
- 2 2 0 0 1
- 3 0 0 1 0
Operations on Multigraph:
Various operations can be performed on a multigraph, including:
- AddVertex(V): Adds a new vertex V to the multigraph.
- AddEdge(V, W): Adds a new edge between vertices V and W in the multigraph.
- DeleteVertex(V): Deletes the vertex V from the multigraph.
- DeleteEdge(V, W): Deletes the edge between vertices V and W from the multigraph.
- GetAdjacentVertices(V): Returns a list of all vertices adjacent to vertex V in the multigraph.
- GetDegree(V): Returns the degree of vertex V, i.e., the number of edges incident to it in the multigraph.
Applications:
Multigraphs find applications in various fields, including network analysis, transportation systems, social networks, and computer science algorithms. They provide a more flexible representation when multiple connections between vertices are required.
In conclusion, understanding multigraphs is crucial for analyzing complex relationships and connectivity patterns in real-world scenarios. By using appropriate data structures and algorithms, we can efficiently represent and manipulate multigraphs to solve a wide range of problems.
10 Related Question Answers Found
A multigraph is a type of graph in data structure that allows multiple edges between two vertices. In other words, it is a graph that can have parallel edges connecting the same pair of vertices. Definition
A multigraph, also known as a pseudograph, is an extension of a simple graph where multiple edges can exist between any two vertices.
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