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Regina 7.3 Calculation Engine
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The namespace regina::graph provides an interface for various types of objects from Regina to work directly with the Boost Graph Library (BGL).
After including the header triangulation/graph.h, any object of type regina::Triangulation<dim> can be used directly as a graph with the BGL. Here the graph will be the dual graph of the triangulation: this is an undirected multigraph in which each node represents a dim-simplex of the triangulation, and each arc represents a gluing between two adjacent dim-simplices.
Triangulations implement several BGL graph concepts, including:
Triangulations are not mutable graphs - for the purposes of the BGL, they are considered read-only.
Dual vertices of the graph represent dim-dimensional simplices of the underlying triangulation, and so are represented directly by a pointer of type regina::Simplex<dim>*. Dual edges (when accessed through the BGL) must come with an orientation, and so are represented by lightweight objects of type regina::graph::DualEdge<dim>.
After including the header link/graph.h, any object of type regina::Link can be used directly as a graph with the BGL. Here the graph will be the underlying 4-valent directed multigraph of the link: every crossing of the link becomes a vertex of the graph, and every directed arc between crossings becomes a directed edge. Zero-crossing unknot components of a link do not appear in this graph at all.
Knots and links implement several BGL graph concepts, including:
Knots and links are not mutable graphs - for the purposes of the BGL, they are considered read-only.
Vertices of the graph are represented directly by a pointer of type regina::Crossing*. Directed edges are represented by lightweight regina::StrandRef objects; see the regina::StrandRef documentation for how a StrandRef object is used to identify a directed arc of the link.