# What Is Multigraph in Data Structure?

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Angela Bailey

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.

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

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:

• 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.