,[c@sFdZddlZddlZddgZddZddZdS(s5Provides explicit constructions of expander graphs. iNtmargulis_gabber_galil_graphtchordal_cycle_graphcCs!tjd|dtj}|js4|j rLd}tj|nxtjt|ddD]\}}x|d|||f|d|d||f||d||f||d|d|ffD](\}}|j ||f||fqWqhWdj ||j d<|S( sReturn the Margulis-Gabber-Galil undirected MultiGraph on `n^2` nodes. The undirected MultiGraph is regular with degree `8`. Nodes are integer pairs. The second-largest eigenvalue of the adjacency matrix of the graph is at most `5 \sqrt{2}`, regardless of `n`. Parameters ---------- n : int Determines the number of nodes in the graph: `n^2`. create_using : NetworkX graph constructor, optional (default MultiGraph) Graph type to create. If graph instance, then cleared before populated. Returns ------- G : graph The constructed undirected multigraph. Raises ------ NetworkXError If the graph is directed or not a multigraph. itdefaults0`create_using` must be an undirected multigraph.trepeatiis margulis_gabber_galil_graph({0})tname( tnxt empty_grapht MultiGrapht is_directedt is_multigrapht NetworkXErrort itertoolstproducttrangetadd_edgetformattgraph(tnt create_usingtGtmsgtxtytutv((s<lib/python2.7/site-packages/networkx/generators/expanders.pyR.s(1>$c Cstjd|dtj}|js4|j rLd}tj|nxt|D]t}|d|}|d|}|dkrt||d|nd}x'|||fD]}|j||qWqYWdj ||j d<|S(sReturn the chordal cycle graph on `p` nodes. The returned graph is a cycle graph on `p` nodes with chords joining each vertex `x` to its inverse modulo `p`. This graph is a (mildly explicit) 3-regular expander [1]_. `p` *must* be a prime number. Parameters ---------- p : a prime number The number of vertices in the graph. This also indicates where the chordal edges in the cycle will be created. create_using : NetworkX graph constructor, optional (default=nx.Graph) Graph type to create. If graph instance, then cleared before populated. Returns ------- G : graph The constructed undirected multigraph. Raises ------ NetworkXError If `create_using` indicates directed or not a multigraph. References ---------- .. [1] Theorem 4.4.2 in A. Lubotzky. "Discrete groups, expanding graphs and invariant measures", volume 125 of Progress in Mathematics. Birkhäuser Verlag, Basel, 1994. iRs0`create_using` must be an undirected multigraph.iischordal_cycle_graph({0})R( RRRRR R R tpowRRR( tpRRRRtlefttrighttchordR((s<lib/python2.7/site-packages/networkx/generators/expanders.pyRTs& ((t__doc__R tnetworkxRt__all__tNoneRR(((s<lib/python2.7/site-packages/networkx/generators/expanders.pyts    # &