hiperwalk.IntegerLattice

hiperwalk.IntegerLattice(dim, basis=None, periodic=True, multiedges=None, weights=None)

Integer lattice graph.

An integer lattice is a lattice in an euclidean space such that every point is a tuple of integers. In the integer lattice graph, every vertex corresponds to a lattice point.

Parameters:

dimtuple of int

Lattice dimensions where dim[i] is the number of vertices in the i-th-axis.

basislist of int or matrix, default=None

Vectors used to determine the graph adjacency and the corresponding order of neighbors. basis can be specified in three different ways. Let n = len(dim).

• None

  Equivalent to the argument [1, ..., n].

• list of int

  Adjacency is described by the standard basis where i corresponds to the array with all entries equal to 0 and the i-1-th entry equal to 1. Analogously, -i corresponds to the same array but in the opposite direction (-1 instead of 1).

  The values of basis must satisfy 1 <= abs(basis) <= n. Note that 0 is not a valid value because -0 == 0.

  It is expected that len(basis) == 2*n or len(basis) == n. If len(basis) == n, the equivalent argument is

  [basis[0], ..., basis[n - 1],
   -basis[0], ..., -basis[n - 1]]
  

• matrix

  A matrix with 2*n rows and n columns. The i-th neighbor of the vertex with coordinates (v[0], ..., v[n-1]) is (v[0] + basis[i][0], ..., v[n-1] + basis[i][n-1]).

periodicbool, default=True

True if the grid has cyclic boundary conditions, False if it has borders.

multiedges, weights: scipy.sparse.csr_array, default=None

See Graph Constructors.

Returns:

hiperwalk.Graph

See Graph Constructors for details.

See also

Graph Constructors

Notes

The order of neighbors depends on the value of basis.

The vertex number depends on its coordinates and dim. If the coordinates of a vertex are (v[0], ..., v[n-1]), its number is v[n-1] + dim[n-1]*v[n-2] + ... + dim[n-1]*...*dim[1]*v[0].

Examples

>>> g = hpw.IntegerLattice((3, 3), basis=None)
>>> neigh = g.neighbors((1, 1))
>>> [tuple(g.vertex_coordinates(v)) for v in neigh]
[(2, 1), (1, 2), (0, 1), (1, 0)]

>>> g = hpw.IntegerLattice((3, 3), basis=[-1, -2])
>>> neigh = g.neighbors((1, 1))
>>> [tuple(g.vertex_coordinates(v)) for v in neigh]
[(0, 1), (1, 0), (2, 1), (1, 2)]

>>> basis = [[0, 1], [-1, 1], [1, -1], [0, -1]]
>>> g = hpw.IntegerLattice((3, 3), basis=basis)
>>> neigh = g.neighbors((1, 1))
>>> [tuple(g.vertex_coordinates(v)) for v in neigh]
[(1, 2), (0, 2), (2, 0), (1, 0)]

Methods

Besides all methods inherited from hiperwalk.Graph, hiperwalk.Multigraph, or hiperwalk.WeightedGraph, an integer lattice instance also has the following method.

dimensions(self)	Dimensions of integer lattice.
vertex_coordinates(self, vertex)	Return the coordinates of the given vertex.