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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 ...
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.
To determine if a causal loop is reinforcing or balancing, one can start with an assumption, e.g. "Variable 1 increases" and follow the loop around. The loop is: reinforcing if, after going around the loop, one ends up with the same result as the initial assumption. balancing if the result contradicts the initial assumption.
A closed loop is a cyclical path of adjacent vertices that never revisits the same vertex. Such a cycle can be thought of as the boundary of a hypothetical 2-cell. The k-labellings of a graph that conserve momentum (i.e. which has zero boundary) up to redefinitions of k (i.e. up to boundaries of 2-cells) define the first homology of a graph ...
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each internal vertex are equal to each other. [ 1 ]
(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.
The same proof can be interpreted as summing the entries of the incidence matrix of the graph in two ways, by rows to get the sum of degrees and by columns to get twice the number of edges. [5] For graphs, the handshaking lemma follows as a corollary of the degree sum formula. [8]
Here are all of the Dynkin graphs for affine groups up to 10 nodes. Extended Dynkin graphs are given as the ~ families, the same as the finite graphs above, with one node added. Other directed-graph variations are given with a superscript value (2) or (3), representing foldings of higher order groups. These are categorized as Twisted affine ...