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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 ...
The graph attention network (GAT) was introduced by Petar Veličković et al. in 2018. [11] Graph attention network is a combination of a GNN and an attention layer. The implementation of attention layer in graphical neural networks helps provide attention or focus to the important information from the data instead of focusing on the whole data.
A drawing of a graph with 6 vertices and 7 edges.. In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
Spectral graph theory is the branch of graph theory that uses spectra to analyze graphs. See also spectral expansion. split 1. A split graph is a graph whose vertices can be partitioned into a clique and an independent set. A related class of graphs, the double split graphs, are used in the proof of the strong perfect graph theorem.
A chain graph is a graph which may have both directed and undirected edges, but without any directed cycles (i.e. if we start at any vertex and move along the graph respecting the directions of any arrows, we cannot return to the vertex we started from if we have passed an arrow). Both directed acyclic graphs and undirected graphs are special ...
A multigraph with multiple edges (red) and several loops (blue). Not all authors allow multigraphs to have loops. In mathematics, and more specifically in graph theory, a multigraph is a graph which is permitted to have multiple edges (also called parallel edges [1]), that is, edges that have the same end nodes.
Undirected hypergraphs are useful in modelling such things as satisfiability problems, [5] databases, [6] machine learning, [7] and Steiner tree problems. [8] They have been extensively used in machine learning tasks as the data model and classifier regularization (mathematics). [9]
A configuration, also called an instantaneous description (ID), is a finite representation of the machine at a given time. For example, for a finite automata and a given input, the configuration will be the current state and the number of read letters, for a Turing machine it will be the state, the content of the tape and the position of the head.