geometric_graph

graph_tool.generation.geometric_graph(points, radius, ranges=None)

Generate a geometric network form a set of N-dimensional points.

Parameters:

pointslist or numpy.ndarray

List of points. This must be a two-dimensional array, where the rows are coordinates in a N-dimensional space.

radiusfloat

Pairs of points with an euclidean distance lower than this parameters will be connected.

rangeslist or numpy.ndarray (optional, default: None)

If provided, periodic boundary conditions will be assumed, and the values of this parameter it will be used as the ranges in all dimensions. It must be a two-dimensional array, where each row will cointain the lower and upper bound of each dimension.

Returns:

geometric_graphGraph

The generated graph.

posVertexPropertyMap

A vertex property map with the position of each vertex.

See also

triangulation

2D or 3D triangulation

random_graph

random graph generation

lattice

N-dimensional square lattice

Notes

A geometric graph [geometric-graph] is generated by connecting points embedded in a N-dimensional euclidean space which are at a distance equal to or smaller than a given radius.

References

[geometric-graph]

Jesper Dall and Michael Christensen, “Random geometric graphs”, Phys. Rev. E 66, 016121 (2002), DOI: 10.1103/PhysRevE.66.016121 [sci-hub, @tor]

Examples

>>> points = random((500, 2)) * 4
>>> g, pos = gt.geometric_graph(points, 0.3)
>>> gt.graph_draw(g, pos=pos, output="geometric.pdf")
<...>

>>> g, pos = gt.geometric_graph(points, 0.3, [(0,4), (0,4)])
>>> pos = gt.graph_draw(g, output="geometric_periodic.pdf")

Left: Geometric network with random points. Right: Same network, but

with periodic boundary conditions.