A multigraph permits distinct edges with the same pair of endpoints. Whether loops are also allowed is a convention that must be specified for a particular result. Counting edges with multiplicity differs from counting adjacent vertices.
A bouquet graph consists of one vertex and self-loops. Its vertex has degree , and its graph excess is . The two-loop bouquet is one of the three possible kernels of a bicyclic graph; in a simple subdivision, each loop must expand to a cycle of length at least three.
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A **multigraph** is a type of graph in graph theory that allows for multiple edges between the same pair of vertices. This means that in a multigraph, it is possible to have two or more edges connecting the same vertices (like A and B) in addition to the regular edges that connect different pairs of vertices. In contrast, a simple graph does not allow multiple edges between the same pair of vertices or self-loops (edges that connect a vertex to itself).