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multigraph
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seven bridges of Königsberg and multigraph. Five diagrams illustrate types of graphs in mathematics: a simple graph, a multigraph with parallel edges, a complete graph with all possible connections, a graph with a loop, and a directed graph with arrows showing direction.
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multigraph

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seven bridges of Königsberg and multigraph.
seven bridges of Königsberg and multigraph. Figure 6: (A) Seven bridges of Königsberg and (B) multigraph.

In mathematics, a multigraph is a type of graph that consists of a set of vertices (points) and a set of edges (lines) connecting these vertices. Unlike a simple graph, a multigraph allows for more than one edge to connect any two vertices. It can also include loops, which are edges that connect a vertex to itself.

The concept of multigraphs is fundamental to graph theory, a branch of mathematics that studies networks. Graph theory has applications in various fields, including chemistry, computer science, and operations research. A key problem in graph theory, the Königsberg bridge problem, was solved by Leonhard Euler in 1735 and demonstrated the principles of Eulerian cycles within multigraphs. An Eulerian cycle is a path that traverses each edge exactly once.123

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3 Britannica Sources
  1. multigraph
  2. graph theory
  3. combinatorics - Eulerian cycles and the Königsberg bridge problem

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