an edge that is between a vertex and itself is a
loop
title: Edge (geometry) text: Edge (geometry) In geometry, an edge is a particular type of line segment joining two vertices in a polygon, polyhedron, or higher-dimensional polytope. In a polygon, an edge is a line segment on the boundary, and is often called a side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal. In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which title: Vertex (geometry) text: Vertex (geometry) In geometry, a vertex (plural: vertices or vertexes) is a point where two or more curves, lines, or edges meet. 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. The "vertex" of an angle is the point where two rays begin or meet, where two line segments join or meet, where two lines intersect (cross), or any appropriate combination of rays, segments and lines that result in two straight "sides" meeting at one place. A vertex is a corner point of a title: Graph (discrete mathematics) text: The "size" of a graph is |"E"|, its number of edges. The "degree" or "valency" of a vertex is the number of edges that connect to it, where an edge that connects to the vertex at both ends (a loop) is counted twice. For an edge }, graph theorists usually use the somewhat shorter notation "xy". The edges "E" of an undirected graph "G" induce a symmetric binary relation ~ on "V" that is called the "adjacency relation" of "G". Specifically, for each edge }, the vertices "x" and "y" are said to be "adjacent" to one another, which is title: Loop (graph theory) text: Loop (graph theory) 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 vertices): In a graph with one vertex, all edges must be loops. Such a graph is called a bouquet. For an undirected graph, the degree of a vertex is equal to the number of adjacent title: Vertex (graph theory) text: a set of vertices no two of which are adjacent, and a vertex cover is a set of vertices that includes at least one endpoint of each edge in the graph. The vertex space of a graph is a vector space having a set of basis vectors corresponding with the graph's vertices. A graph is vertex-transitive if it has symmetries that map any vertex to any other vertex. In the context of graph enumeration and graph isomorphism it is important to distinguish between labeled vertices and unlabeled vertices. A labeled vertex is a vertex that is associated with extra information