- pegasus_torus(m, node_list=None, edge_list=None, offset_lists=None, offsets_index=None)¶
Creates a Pegasus graph modified to allow for periodic boundary conditions and translational invariance.
m (int) – Size parameter for the Pegasus lattice. Connectivity of all nodes is \(13 + min(m - 1, 2)\)
node_list (iterable (optional, default None)) – Iterable of nodes in the graph. If None, nodes are generated for an undiluted torus calculated from
mas described below. The node list must describe a subset of the torus nodes to be maintained in the graph using the coordinate node labeling scheme.
edge_list (iterable (optional, default None)) – Iterable of edges in the graph. If None, edges are generated for an undiluted torus calculated from
mas described below. The edge list must describe a subgraph of the torus, using the coordinate node labeling scheme.
offset_lists (pair of lists, optional (default None)) – Directly controls the offsets. Each list in the pair must have length 12 and contain even integers. If
offset_listsis not None, the
offsets_indexparameter must be None.
offsets_index (int, optional (default None)) – A number between 0 and 7, inclusive, that selects a preconfigured set of topological parameters. If both the
offset_listsparameters are None, the
offsets_indexparameters is set to zero. At least one of these two parameters must be None.
G – A Pegasus torus for size parameter \(m\) using the coordinate labeling system.
- Return type
A Pegasus torus is a generalization of the standard Pegasus graph whereby degree-fifteen connectivity is maintained, but the boundary condition is modified to enforce an additional translational-invariance symmetry [RH]. Local connectivity in the Pegasus torus is identical to connectivity for Pegasus graph nodes away from the boundary. A tile consists of 24 nodes, and the torus has \(m - 1\) by \(m - 1\) tiles. Tile displacement modulo \(m - 1\) defines an automorphism.
pegasus_graph()for additional information.
>>> G = dnx.pegasus_torus(4) # a 3x3 tile pegasus torus (connectivity 15) >>> len(G) # 3*3*24 216 >>> any([len(list(G.neighbors(n))) != 15 for n in G.nodes]) False