Loop ( graph Theory ) - wikipedia Loop ( graph Theory ) A graph with a loop on vertex 1 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 ) : Where graphs are defined so as to allow loops and multiple edges, a graph without loops or multiple edges is often distinguished from other graphs by calling it a `` simple graph ''. Where graphs are defined so as to disallow loops and multiple edges, a graph that does have loops or multiple edges is often distinguished from the graphs that satisfy these constraints by calling it a `` multigraph '' or `` pseudograph ''. In a graph with one vertex, all edges must be loops. Such a graph is called a bouquet. Contents 1 Degree 2 See also 3 References 4 External links Degree For an undirected graph, the degree of a vertex is equal to the number of adjacent vertices. A special case is a loop, which adds two to the degree. This can be understood by letting each connection of the loop edge count as its own adjacent vertex. In other words, a vertex with a loop `` sees '' itself as an adjacent vertex from both ends of the edge thus adding two, not one, to the degree. For a directed graph, a loop adds one to the in degree and one to the out degree. See also Loops in Graph Theory Cycle ( graph theory ) Graph theory Glossary of graph theory Loops in Topology Möbius ladder Möbius strip Strange loop Klein bottle References Balakrishnan, V.K. ; Graph Theory, McGraw - Hill ; 1 edition ( February 1, 1997 ). ISBN 0 - 07 - 005489 - 4. Bollobás, Béla ; Modern Graph Theory, Springer ; 1st edition ( August 12, 2002 ). ISBN 0 - 387 - 98488 - 7. Diestel, Reinhard ; Graph Theory, Springer ; 2nd edition ( February 18, 2000 ). ISBN 0 - 387 - 98976 - 5. Gross, Jonathon L, and Yellen, Jay ; Graph Theory and Its Applications, CRC Press ( December 30, 1998 ). ISBN 0 - 8493 - 3982 - 0. Gross, Jonathon L, and Yellen, Jay ; ( eds ) ; Handbook of Graph Theory. CRC ( December 29, 2003 ). ISBN 1 - 58488 - 090 - 2. Zwillinger, Daniel ; CRC Standard Mathematical Tables and Formulae, Chapman & Hall / CRC ; 31st edition ( November 27, 2002 ). ISBN 1 - 58488 - 291 - 3. External links This article incorporates public domain material from the NIST document : Black, Paul E. `` Self loop ''. Dictionary of Algorithms and Data Structures. Retrieved from `` https://en.wikipedia.org/w/index.php?title=Loop_(graph_theory)&oldid=815655329 '' Categories : Graph theory Talk Contents About Wikipedia Català Deutsch Español Esperanto Français Polski Português Русский Simple English Українська 3 more Edit links This page was last edited on 16 December 2017, at 05 : 43. About Wikipedia

Question: an edge that is between a vertex and itself is a
Answer: loop (also called a self-loop or a "buckle"); loop; loop; loop; loop