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In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering ( software construction and also software verification ) to layout algorithms and picture generation.
In summary, GSS (Graph Style Sheets) have been designed for the purpose of filtering, grouping and styling of information elements through specification of declarative transformation rules. [ 1 ] GSS not only associate styles to node-edge representation of RDF models, but also can be used to hide part of the graph and offer alternative layouts ...
The transformation of graphs is often formalized and represented by graph rewrite systems. Complementary to graph transformation systems focusing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data.
ΔY- and YΔ-transformations are a tool both in pure graph theory as well as applications. Both operations preserve a number of natural topological properties of graphs. . For example, applying a YΔ-transformation to a 3-vertex of a planar graph, or a ΔY-transformation to a triangular face of a planar graph, results again in a planar graph.
The reciprocal transformation, some power transformations such as the Yeo–Johnson transformation, and certain other transformations such as applying the inverse hyperbolic sine, can be meaningfully applied to data that include both positive and negative values [10] (the power transformation is invertible over all real numbers if λ is an odd ...
Affine transformation (Euclidean geometry); Bäcklund transform; Bilinear transform; Box–Muller transform; Burrows–Wheeler transform (data compression); Chirplet transform ...
Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is important in spectral graph theory. It is widely applied in the recent study of graph structured learning algorithms, such as the widely employed convolutional networks.
By combining these two results, it may be shown that every triangle-free planar graph has a homomorphism to a triangle-free 3-colorable graph, the tensor product of with the Clebsch graph. The coloring of the graph may then be recovered by composing this homomorphism with the homomorphism from this tensor product to its K 3 {\displaystyle K_{3 ...