Multigráfról

A multigráfról, often referred to as a multigraph, is a type of graph in graph theory that generalizes the concept of a simple graph. In a simple graph, there is at most one edge between any two distinct vertices, and no edge connects a vertex to itself (no loops). A multigráfról relaxes these restrictions, allowing for multiple edges between the same pair of vertices and also permitting edges that connect a vertex to itself, known as loops.

The presence of multiple edges between two vertices means that the connection between them is not unique. For instance, in a transportation network, multiple edges could represent different routes or modes of transport between two cities. Loops, on the other hand, represent a connection from a vertex back to itself, which can model self-relationships or internal processes within a node.

Multigráfról are useful in various applications where the simple graph model is insufficient. They can be used to represent situations with parallel connections, such as communication networks with redundant links, or chemical reactions where multiple pathways exist between reactants. In computer science, they can model data structures or processes with self-referential properties. The mathematical analysis of multigráfról often involves adapting algorithms and theorems developed for simple graphs to accommodate the additional complexity introduced by multiple edges and loops. For example, concepts like connectivity and paths need to be redefined or carefully interpreted in the context of a multigráfról.