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based on an earlier version of the Wolfram Language.
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Graph Programming
By providing a completely extensible set of vertex and edge properties, you can make graphs represent much more than the structural information embodied in their topology. For instance, vertices could contain dynamic system models and edges could contain signals, and the graph could then represent a block-diagram model. The vertex and edge properties can also be used to store the state when scanning the graph in a depth-first or breadth-first manner as used by many graph algorithms. But Mathematica provides a multi-paradigm approach to graph programming with a rich set of matrix, optimization, and Boolean-based frameworks that allow for a variety of extensions to the whole graph framework.
Manipulating Vertex and Edge Properties
Property property wrapper for vertices and edges
Properties option for graphs to specify vertex and edge properties
PropertyList give a list of available properties
PropertyValue get and set vertex or edge property values
Scan-Based Algorithms
BreadthFirstScan scan a graph in a breadth-first order
DepthFirstScan scan a graph in a depth-first order
  ▪   ▪   ▪   ▪   ▪   ▪   ▪
AdjacencyMatrix convert to a sparse adjacency matrix representation
AdjacencyGraph construct a graph from an adjacency matrix
Transpose  ▪ Dot  ▪ Eigenvalues  ▪ Eigenvectors  ▪ ...
Minimize minimize a function with constraints
SatisfiableQ test whether a Boolean formula or function can be True
TautologyQ  ▪ Conjunction  ▪ Disjunction  ▪ ...
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