Multigraph

A multigraph is a graph that permits multiple edges between the same pair of vertices. Depending on convention, it may also permit loops.

Graph (discrete mathematics): A graph is a structure consisting of vertices and edges that connect pairs of vertices. A multigraph extends this broader structure by allowing repeated edges.
Adjacency matrix: An adjacency matrix records vertex connections in a square matrix indexed by vertices. Its entries can count the number of edges between each pair of vertices.
Simple graph: A simple graph has no loops and at most one edge between any pair of distinct vertices. It excludes both features that distinguish common multigraph conventions.
Transportation network: A transportation network is a system of locations linked by routes or services. Several routes can connect the same two locations, producing parallel edges.
Vertex (graph theory): A vertex is a fundamental element of a graph, representing an object or position. Multiple edges in a multigraph connect the same pair of vertices.
Incidence matrix: An incidence matrix records which vertices are incident to which edges. Separate columns preserve the identity of parallel edges.
Pseudograph: A pseudograph is a graph that permits loops and multiple edges between vertices. Terminology varies: this name often reserves multigraph for graphs without loops.
Electrical circuit: An electrical circuit is an interconnected system of components that provides paths for electric current. Distinct components or branches can connect the same pair of junctions.
Edge (graph theory): An edge is a connection between vertices in a graph. A multigraph can contain distinct edges with identical endpoints.
Line graph: A line graph represents each edge of a graph as a vertex, connecting vertices for incident edges. Distinct parallel edges become distinct adjacent vertices in the line graph.

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