Title: Edge (geometry)
Content:  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 polygon side. In a polyhedron or more generally a polytope, an edge is a line segment where two faces (or polyhedron sides) meet. A segment joining two vertices while passing through the interior or exterior is not an edge but instead is called a diagonal.
Title: Edge (geometry)
Content:  In graph theory, an edge is an abstract object connecting two graph vertices, unlike polygon and polyhedron edges which have a concrete geometric representation as a line segment. However, any polyhedron can be represented by its skeleton or edge-skeleton, a graph whose vertices are the geometric vertices of the polyhedron and whose edges correspond to the geometric edges. Conversely, the graphs that are skeletons of three-dimensional polyhedra can be characterized by Steinitz's theorem as being exactly the 3-vertex-connected planar graphs.
Title: Vertex (graph theory)
Content:  as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex w is said to be adjacent to another vertex v if the graph contains an edge (v,w). The neighborhood of a vertex v is an induced subgraph of the graph, formed by all vertices adjacent to v.
Title: Graph (discrete mathematics)
Content:  Two edges of a graph are called adjacent if they share a common vertex. Two edges of a directed graph are called consecutive if the head of the first one is the tail of the second one. Similarly, two vertices are called adjacent if they share a common edge (consecutive if the first one is the tail and the second one is the head of an edge), in which case the common edge is said to join the two vertices. An edge and a vertex on that edge are called incident. The graph with only one vertex and no edges 
Title: Degree (graph theory)
Content: A vertex with degree 0 is called an isolated vertex. ; A vertex with degree 1 is called a leaf vertex or end vertex, and the edge incident with that vertex is called a pendant edge. In the graph on the right, {3,5} is a pendant edge. This terminology is common in the study of trees in graph theory and especially trees as data structures. ; A vertex with degree n &minus; 1 in a graph on n vertices is called a dominating vertex. 
Title: Vertex (graph theory)
Content:  The degree of a vertex, denoted 𝛿(v) in a graph is the number of edges incident to it. An isolated vertex is a vertex with degree zero; that is, a vertex that is not an endpoint of any edge (the example image illustrates one isolated vertex). A leaf vertex (also pendant vertex) is a vertex with degree one. In a directed graph, one can distinguish the outdegree (number of outgoing edges), denoted 𝛿+(v), from the indegree (number of incoming edges), denoted 𝛿−(v); a source vertex is a vertex with indegree zero, while a sink vertex is a vertex with outdegree zero. A simplicial vertex 
Title: Vertex (geometry)
Content:  In geometry, a vertex (in plural form: vertices or vertexes), often denoted by letters such as, 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.
Title: Vertex (graph theory)
Content:  In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are 
Title: Vertex (geometry)
Content:  A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object. In a polygon, a vertex is called "convex" if the internal angle of the polygon (i.e., the angle formed by the two edges at the vertex with the polygon inside the angle) is less than π radians (180°, two right angles); otherwise, it is called "concave" or "reflex". More generally, a vertex of a polyhedron or polytope is convex, if the intersection of the polyhedron or polytope with a sufficiently small sphere centered at the vertex is convex, and is concave otherwise. Polytope vertices are related to vertices of graphs, in that the 1-skeleton of a polytope is a graph, 
Title: Top tree
Content:  A vertex in a connected subtree is a Boundary Vertex if it is connected to a vertex outside the subtree by an edge.

Question: an edge that is between a vertex and itself is a?
Answer: loop.