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Multiple edges joining two vertices. In graph theory, multiple edges (also called parallel edges or a multi-edge), are, in an undirected graph, two or more edges that are incident to the same two vertices, or in a directed graph, two or more edges with both the same tail vertex and the same head vertex. A simple graph has no multiple edges and ...
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [5] a directed graph is an ordered triple = (,,) comprising: , a set of vertices (also called nodes or points);
The edge (y, x) is called the inverted edge of (x, y). Multiple edges, not allowed under the definition above, are two or more edges with both the same tail and the same head. In one more general sense of the term allowing multiple edges, [8] a directed graph is sometimes defined to be an ordered triple G = (V, E, ϕ) comprising:
In graph theory, a loop (also called a self-loop or a buckle) is an edge that connects a vertex to itself. A simple graph contains no loops. Depending on the context, a graph or a multigraph may be defined so as to either allow or disallow the presence of loops (often in concert with allowing or disallowing multiple edges between the same ...
A multiple adjacency or multiple edge is a set of more than one edge that all have the same endpoints (in the same direction, in the case of directed graphs). A graph with multiple edges is often called a multigraph. multiplicity The multiplicity of an edge is the number of edges in a multiple adjacency.
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of ... Multigraph – Graph with multiple edges between two vertices;
A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines. It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges, links or lines.