Depending on the context, a graph may be defined so as to either allow or disallow the presence of multiple edges (often in concert with allowing or disallowing loops):
Where graphs are defined so as to allow multiple edges and loops, a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph.[1]
Where graphs are defined so as to disallow multiple edges and loops, a multigraph or a pseudograph is often defined to mean a "graph" which can have multiple edges.[2]
Multiple edges are, for example, useful in the consideration of electrical networks, from a graph theoretical point of view.[3] Additionally, they constitute the core differentiating feature of multidimensional networks.
A planar graph remains planar if an edge is added between two vertices already joined by an edge; thus, adding multiple edges preserves planarity.[4]
A dipole graph is a graph with two vertices, in which all edges are parallel to each other.
Notesedit
^For example, see Balakrishnan, p. 1, and Gross (2003), p. 4, Zwillinger, p. 220.
^For example, see Bollobás, p. 7; Diestel, p. 28; Harary, p. 10.
Gross, Jonathon L, and Yellen, Jay; Graph Theory and Its Applications, CRC Press (December 30, 1998). ISBN0-8493-3982-0.
Gross, Jonathon L, and Yellen, Jay; (eds); Handbook of Graph Theory. CRC (December 29, 2003). ISBN1-58488-090-2.
Zwillinger, Daniel; CRC Standard Mathematical Tables and Formulae, Chapman & Hall/CRC; 31st edition (November 27, 2002). ISBN1-58488-291-3.
January 01, 1970
multiple, edges, graph, theory, multiple, edges, also, called, parallel, edges, multi, edge, undirected, graph, more, edges, that, incident, same, vertices, directed, graph, more, edges, with, both, same, tail, vertex, same, head, vertex, simple, graph, multip. 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 no loops Multiple edges joining two vertices Depending on the context a graph may be defined so as to either allow or disallow the presence of multiple edges often in concert with allowing or disallowing loops Where graphs are defined so as to allow multiple edges and loops a graph without loops or multiple edges is often distinguished from other graphs by calling it a simple graph 1 Where graphs are defined so as to disallow multiple edges and loops a multigraph or a pseudograph is often defined to mean a graph which can have multiple edges 2 Multiple edges are for example useful in the consideration of electrical networks from a graph theoretical point of view 3 Additionally they constitute the core differentiating feature of multidimensional networks A planar graph remains planar if an edge is added between two vertices already joined by an edge thus adding multiple edges preserves planarity 4 A dipole graph is a graph with two vertices in which all edges are parallel to each other Notes edit For example see Balakrishnan p 1 and Gross 2003 p 4 Zwillinger p 220 For example see Bollobas p 7 Diestel p 28 Harary p 10 Bollobas pp 39 40 Gross 1998 p 308 References editBalakrishnan V K Graph Theory McGraw Hill 1 edition February 1 1997 ISBN 0 07 005489 4 Bollobas Bela 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 amp Hall CRC 31st edition November 27 2002 ISBN 1 58488 291 3 Retrieved from https en wikipedia org w index php title Multiple edges amp oldid 1145910719, wikipedia, wiki, book, books, library,
