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GMTE Archived 2018-03-13 at the Wayback Machine, the Graph Matching and Transformation Engine for graph matching and transformation. It is an implementation of an extension of Messmer’s algorithm using C++. GrGen.NET, the graph rewrite generator, a graph transformation tool emitting C#-code or .NET-assemblies.
In the lower plot, both the area and population data have been transformed using the logarithm function. In statistics, data transformation is the application of a deterministic mathematical function to each point in a data set—that is, each data point z i is replaced with the transformed value y i = f(z i), where f is a function.
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.
Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.
The definition of convolution between two functions and cannot be directly applied to graph signals, because the signal translation is not defined in the context of graphs. [4] However, by replacing the complex exponential shift in classical Fourier transform with the graph Laplacian eigenvectors, convolution of two graph signals can be defined ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function , which is defined by the formula: [ 1 ]
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form y = a x k {\displaystyle y=ax^{k}} – appear as straight lines in a log–log graph, with the exponent corresponding to ...