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In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. [1] In a polygon, an edge is a line segment on the boundary, [2] and is often called a polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides ...
In geometry, a vertex (pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices. [1] [2] [3]
In geometry, a polygon (/ ˈ p ɒ l ɪ ɡ ɒ n /) is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides. The points where two edges meet are the polygon's vertices or corners. An n-gon is a polygon with n sides; for example, a triangle is a 3 ...
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 graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
The definition above generalizes from a directed graph to a directed hypergraph by defining the head or tail of each edge as a set of vertices (or ) rather than as a single vertex. A graph is then the special case where each of these sets contains only one element.
Under this definition, multiple edges, in which two or more edges connect the same vertices, are not allowed. Example of an undirected multigraph with 3 vertices, 3 edges and 4 loops. For vertices A,B,C and D, the degrees are respectively 4,4,5,1
An edge that connects vertices x and y is sometimes written xy. edge cut A set of edge s whose removal disconnects the graph. A one-edge cut is called a bridge, isthmus, or cut edge. edge set The set of edges of a given graph G, sometimes denoted by E(G). edgeless graph