multigraph
loops and/or multiple edges are allowed
A multigraph is a type of graph in discrete mathematics that allows multiple edges (or edges with the same endpoints) and self-loops (edges that connect a vertex to itself) between two vertices. This means that two vertices in a multigraph can be connected by more than one edge.
In a multigraph, each edge is characterized by its two endpoints and a weight value (if it is weighted). Therefore, if there are multiple edges connecting two vertices, each edge would have a different weight value.
Multigraphs are used to model various real-life scenarios, such as road networks, social networks, and computer networks. They are also used in mathematical problems involving optimization, flow theory, and path-finding algorithms.
To represent a multigraph mathematically, we use a set of vertices (or nodes) and a set of edges connecting the vertices. A multigraph can be represented using an adjacency matrix or an adjacency list. In an adjacency matrix, the rows and columns represent vertices, and the values in each entry represent the weight of the corresponding edge (or 0 if there is no edge). In an adjacency list, each vertex is associated with a list of edges that connect it to other vertices.
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