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In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries. Formally, an automorphism of a graph is a permutation p of its vertices with the property that any two vertices u and v are adjacent if and only if p ( u ) and p ( v ) are adjacent.
Two-frequency beats of a non-dispersive transverse wave. Since the wave is non-dispersive, phase and group velocities are equal. For an ideal string, the dispersion relation can be written as =, where T is the tension force in the string, and μ is the string's mass per unit length. As for the case of electromagnetic waves in vacuum, ideal ...
In the context of network theory, a complex network is a graph (network) with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in networks representing real systems.
Operations between graphs include evaluating the direction of a subsumption relationship between two graphs, if any, and computing graph unification. The unification of two argument graphs is defined as the most general graph (or the computation thereof) that is consistent with (i.e. contains all of the information in) the inputs, if such a ...
An asymmetric graph is an undirected graph with only the trivial automorphism. A vertex-transitive graph is an undirected graph in which every vertex may be mapped by an automorphism into any other vertex. An edge-transitive graph is an undirected graph in which every edge may be mapped by an automorphism into any other edge.
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 graph theory, the trivial graph is a graph which has only 1 vertex and no edge. Database theory has a concept called functional dependency, written . The dependence is true if Y is a subset of X, so this type of dependence is called "trivial". All other dependences, which are less obvious, are called "nontrivial".
The Laplacian matrix of a directed graph is by definition generally non-symmetric, while, e.g., traditional spectral clustering is primarily developed for undirected graphs with symmetric adjacency and Laplacian matrices. A trivial approach to applying techniques requiring the symmetry is to turn the original directed graph into an undirected ...