World Library  
Flag as Inappropriate
Email this Article

Loop (graph theory)

Article Id: WHEBN0001449083
Reproduction Date:

Title: Loop (graph theory)  
Author: World Heritage Encyclopedia
Language: English
Subject: Graph theory, Graph (mathematics), Network science, Self-healing ring, Colin de Verdière graph invariant
Collection: Graph Theory
Publisher: World Heritage Encyclopedia

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".


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

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.

Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.