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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 ...
Directed graphs as defined in the two definitions above cannot have loops, because a loop joining a vertex to itself is the edge (for a directed simple graph) or is incident on (for a directed multigraph) (,) which is not in {(,) (,)}. So to allow loops the definitions must be expanded.
A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).
In mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. It is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.
The same concept can be extended to multigraphs and graphs with loops by storing the number of edges between each two vertices in the corresponding matrix element, and by allowing nonzero diagonal elements. Loops may be counted either once (as a single edge) or twice (as two vertex-edge incidences), as long as a consistent convention is followed.
(d) an irreducible CFG: a loop with two entry points, e.g. goto into a while or for loop A control-flow graph used by the Rust compiler to perform codegen. In computer science, a control-flow graph (CFG) is a representation, using graph notation, of all paths that might be traversed through a program during its execution.
In the picture, the red graphs are not isomorphic because the two vertices with self loops share an edge in one graph but not in the other. Every 4-regular plane graph is the medial graph of some plane graph. For a connected 4-regular plane graph H, a planar graph G with H as its medial graph can be
Diagrams with loops (in graph theory, these kinds of loops are called cycles, while the word loop is an edge connecting a vertex with itself) correspond to the quantum corrections to the classical field theory. Because one-loop diagrams only contain one cycle, they express the next-to-classical contributions called the semiclassical contributions.