In mathematics, a multigraph or pseudograph is a graph which is permitted to have multiple edges, (also called "parallel edges"), that is, edges that have the same end nodes. Thus two vertices may be connected by more than one edge.

There are two distinct notions of multiple edges. One says that, as in graphs without multiple edges, the identity of an edge is defined by the nodes it connects, but the same edge can occur several times between these nodes. Alternatively, one defines edges to be first-class entities like nodes, each having its own identity independent of the nodes it connects.

Formally, a multigraph G is an ordered pair G:=(V, E) with

Multigraphs might be used to model the possible flight connections offered by an airline. In this case the multigraph would be a directed graph with pairs of directed parallel edges connecting cities to show that it is possible to fly both to and from these locations.

Some authors also allow multigraphs to have loops, that is, an edge that connects a vertex to itself, while others call these pseudographs, reserving the term multigraph for the case with no loops.