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GrGen.NET, the graph rewrite generator, a graph transformation tool emitting C#-code or .NET-assemblies. GROOVE, a Java-based tool set for editing graphs and graph transformation rules, exploring the state spaces of graph grammars, and model checking those state spaces; can also be used as a graph transformation engine.
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Double pushout graph rewriting allows the specification of graph transformations by specifying a pattern of fixed size and composition to be found and replaced, where part of the pattern can be preserved. The application of a rule is potentially non-deterministic: several distinct matches can be possible.
The core of the languages consists of modular graph rewrite rules, which are built on declarative graph pattern matching and rewriting; they are supplemented by many of the constructs that are used in imperative and object-oriented programming, and are completed with language devices known from database query languages.
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.
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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] = + = + = ().