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Diffstat (limited to 'lib/python2.7/site-packages/setoolsgui/networkx/algorithms/distance_regular.py')
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diff --git a/lib/python2.7/site-packages/setoolsgui/networkx/algorithms/distance_regular.py b/lib/python2.7/site-packages/setoolsgui/networkx/algorithms/distance_regular.py deleted file mode 100644 index 3fbcdbc..0000000 --- a/lib/python2.7/site-packages/setoolsgui/networkx/algorithms/distance_regular.py +++ /dev/null @@ -1,179 +0,0 @@ -""" -======================= -Distance-regular graphs -======================= -""" -# Copyright (C) 2011 by -# Dheeraj M R <dheerajrav@gmail.com> -# Aric Hagberg <aric.hagberg@gmail.com> -# All rights reserved. -# BSD license. -import networkx as nx -__author__ = """\n""".join(['Dheeraj M R <dheerajrav@gmail.com>', - 'Aric Hagberg <aric.hagberg@gmail.com>']) - -__all__ = ['is_distance_regular','intersection_array','global_parameters'] - -def is_distance_regular(G): - """Returns True if the graph is distance regular, False otherwise. - - A connected graph G is distance-regular if for any nodes x,y - and any integers i,j=0,1,...,d (where d is the graph - diameter), the number of vertices at distance i from x and - distance j from y depends only on i,j and the graph distance - between x and y, independently of the choice of x and y. - - Parameters - ---------- - G: Networkx graph (undirected) - - Returns - ------- - bool - True if the graph is Distance Regular, False otherwise - - Examples - -------- - >>> G=nx.hypercube_graph(6) - >>> nx.is_distance_regular(G) - True - - See Also - -------- - intersection_array, global_parameters - - Notes - ----- - For undirected and simple graphs only - - References - ---------- - .. [1] Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. - Distance-Regular Graphs. New York: Springer-Verlag, 1989. - .. [2] Weisstein, Eric W. "Distance-Regular Graph." - http://mathworld.wolfram.com/Distance-RegularGraph.html - - """ - try: - a=intersection_array(G) - return True - except nx.NetworkXError: - return False - -def global_parameters(b,c): - """Return global parameters for a given intersection array. - - Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d - such that for any 2 vertices x,y in G at a distance i=d(x,y), there - are exactly c_i neighbors of y at a distance of i-1 from x and b_i - neighbors of y at a distance of i+1 from x. - - Thus, a distance regular graph has the global parameters, - [[c_0,a_0,b_0],[c_1,a_1,b_1],......,[c_d,a_d,b_d]] for the - intersection array [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] - where a_i+b_i+c_i=k , k= degree of every vertex. - - Parameters - ---------- - b,c: tuple of lists - - Returns - ------- - p : list of three-tuples - - Examples - -------- - >>> G=nx.dodecahedral_graph() - >>> b,c=nx.intersection_array(G) - >>> list(nx.global_parameters(b,c)) - [(0, 0, 3), (1, 0, 2), (1, 1, 1), (1, 1, 1), (2, 0, 1), (3, 0, 0)] - - References - ---------- - .. [1] Weisstein, Eric W. "Global Parameters." - From MathWorld--A Wolfram Web Resource. - http://mathworld.wolfram.com/GlobalParameters.html - - See Also - -------- - intersection_array - """ - d=len(b) - ba=b[:] - ca=c[:] - ba.append(0) - ca.insert(0,0) - k = ba[0] - aa = [k-x-y for x,y in zip(ba,ca)] - return zip(*[ca,aa,ba]) - - -def intersection_array(G): - """Returns the intersection array of a distance-regular graph. - - Given a distance-regular graph G with integers b_i, c_i,i = 0,....,d - such that for any 2 vertices x,y in G at a distance i=d(x,y), there - are exactly c_i neighbors of y at a distance of i-1 from x and b_i - neighbors of y at a distance of i+1 from x. - - A distance regular graph'sintersection array is given by, - [b_0,b_1,.....b_{d-1};c_1,c_2,.....c_d] - - Parameters - ---------- - G: Networkx graph (undirected) - - Returns - ------- - b,c: tuple of lists - - Examples - -------- - >>> G=nx.icosahedral_graph() - >>> nx.intersection_array(G) - ([5, 2, 1], [1, 2, 5]) - - References - ---------- - .. [1] Weisstein, Eric W. "Intersection Array." - From MathWorld--A Wolfram Web Resource. - http://mathworld.wolfram.com/IntersectionArray.html - - - See Also - -------- - global_parameters - """ - if G.is_multigraph() or G.is_directed(): - raise nx.NetworkxException('Not implemented for directed ', - 'or multiedge graphs.') - # test for regular graph (all degrees must be equal) - degree = G.degree_iter() - (_,k) = next(degree) - for _,knext in degree: - if knext != k: - raise nx.NetworkXError('Graph is not distance regular.') - k = knext - path_length = nx.all_pairs_shortest_path_length(G) - diameter = max([max(path_length[n].values()) for n in path_length]) - bint = {} # 'b' intersection array - cint = {} # 'c' intersection array - for u in G: - for v in G: - try: - i = path_length[u][v] - except KeyError: # graph must be connected - raise nx.NetworkXError('Graph is not distance regular.') - # number of neighbors of v at a distance of i-1 from u - c = len([n for n in G[v] if path_length[n][u]==i-1]) - # number of neighbors of v at a distance of i+1 from u - b = len([n for n in G[v] if path_length[n][u]==i+1]) - # b,c are independent of u and v - if cint.get(i,c) != c or bint.get(i,b) != b: - raise nx.NetworkXError('Graph is not distance regular') - bint[i] = b - cint[i] = c - return ([bint.get(i,0) for i in range(diameter)], - [cint.get(i+1,0) for i in range(diameter)]) - - |