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Diffstat (limited to 'lib/python2.7/site-packages/setoolsgui/networkx/generators/small.py')
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diff --git a/lib/python2.7/site-packages/setoolsgui/networkx/generators/small.py b/lib/python2.7/site-packages/setoolsgui/networkx/generators/small.py new file mode 100644 index 0000000..f41f8d0 --- /dev/null +++ b/lib/python2.7/site-packages/setoolsgui/networkx/generators/small.py @@ -0,0 +1,412 @@ +# -*- coding: utf-8 -*- +""" +Various small and named graphs, together with some compact generators. + +""" +__author__ ="""Aric Hagberg (hagberg@lanl.gov)\nPieter Swart (swart@lanl.gov)""" +# Copyright (C) 2004-2008 by +# Aric Hagberg <hagberg@lanl.gov> +# Dan Schult <dschult@colgate.edu> +# Pieter Swart <swart@lanl.gov> +# All rights reserved. +# BSD license. + +__all__ = ['make_small_graph', + 'LCF_graph', + 'bull_graph', + 'chvatal_graph', + 'cubical_graph', + 'desargues_graph', + 'diamond_graph', + 'dodecahedral_graph', + 'frucht_graph', + 'heawood_graph', + 'house_graph', + 'house_x_graph', + 'icosahedral_graph', + 'krackhardt_kite_graph', + 'moebius_kantor_graph', + 'octahedral_graph', + 'pappus_graph', + 'petersen_graph', + 'sedgewick_maze_graph', + 'tetrahedral_graph', + 'truncated_cube_graph', + 'truncated_tetrahedron_graph', + 'tutte_graph'] + +import networkx as nx +from networkx.generators.classic import empty_graph, cycle_graph, path_graph, complete_graph +from networkx.exception import NetworkXError + +#------------------------------------------------------------------------------ +# Tools for creating small graphs +#------------------------------------------------------------------------------ +def make_small_undirected_graph(graph_description, create_using=None): + """ + Return a small undirected graph described by graph_description. + + See make_small_graph. + """ + if create_using is not None and create_using.is_directed(): + raise NetworkXError("Directed Graph not supported") + return make_small_graph(graph_description, create_using) + +def make_small_graph(graph_description, create_using=None): + """ + Return the small graph described by graph_description. + + graph_description is a list of the form [ltype,name,n,xlist] + + Here ltype is one of "adjacencylist" or "edgelist", + name is the name of the graph and n the number of nodes. + This constructs a graph of n nodes with integer labels 0,..,n-1. + + If ltype="adjacencylist" then xlist is an adjacency list + with exactly n entries, in with the j'th entry (which can be empty) + specifies the nodes connected to vertex j. + e.g. the "square" graph C_4 can be obtained by + + >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[1,3],[2,4],[1,3]]]) + + or, since we do not need to add edges twice, + + >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[3],[4],[]]]) + + If ltype="edgelist" then xlist is an edge list + written as [[v1,w2],[v2,w2],...,[vk,wk]], + where vj and wj integers in the range 1,..,n + e.g. the "square" graph C_4 can be obtained by + + >>> G=nx.make_small_graph(["edgelist","C_4",4,[[1,2],[3,4],[2,3],[4,1]]]) + + Use the create_using argument to choose the graph class/type. + """ + ltype=graph_description[0] + name=graph_description[1] + n=graph_description[2] + + G=empty_graph(n, create_using) + nodes=G.nodes() + + if ltype=="adjacencylist": + adjlist=graph_description[3] + if len(adjlist) != n: + raise NetworkXError("invalid graph_description") + G.add_edges_from([(u-1,v) for v in nodes for u in adjlist[v]]) + elif ltype=="edgelist": + edgelist=graph_description[3] + for e in edgelist: + v1=e[0]-1 + v2=e[1]-1 + if v1<0 or v1>n-1 or v2<0 or v2>n-1: + raise NetworkXError("invalid graph_description") + else: + G.add_edge(v1,v2) + G.name=name + return G + + +def LCF_graph(n,shift_list,repeats,create_using=None): + """ + Return the cubic graph specified in LCF notation. + + LCF notation (LCF=Lederberg-Coxeter-Fruchte) is a compressed + notation used in the generation of various cubic Hamiltonian + graphs of high symmetry. See, for example, dodecahedral_graph, + desargues_graph, heawood_graph and pappus_graph below. + + n (number of nodes) + The starting graph is the n-cycle with nodes 0,...,n-1. + (The null graph is returned if n < 0.) + + shift_list = [s1,s2,..,sk], a list of integer shifts mod n, + + repeats + integer specifying the number of times that shifts in shift_list + are successively applied to each v_current in the n-cycle + to generate an edge between v_current and v_current+shift mod n. + + For v1 cycling through the n-cycle a total of k*repeats + with shift cycling through shiftlist repeats times connect + v1 with v1+shift mod n + + The utility graph K_{3,3} + + >>> G=nx.LCF_graph(6,[3,-3],3) + + The Heawood graph + + >>> G=nx.LCF_graph(14,[5,-5],7) + + See http://mathworld.wolfram.com/LCFNotation.html for a description + and references. + + """ + if create_using is not None and create_using.is_directed(): + raise NetworkXError("Directed Graph not supported") + + if n <= 0: + return empty_graph(0, create_using) + + # start with the n-cycle + G=cycle_graph(n, create_using) + G.name="LCF_graph" + nodes=G.nodes() + + n_extra_edges=repeats*len(shift_list) + # edges are added n_extra_edges times + # (not all of these need be new) + if n_extra_edges < 1: + return G + + for i in range(n_extra_edges): + shift=shift_list[i%len(shift_list)] #cycle through shift_list + v1=nodes[i%n] # cycle repeatedly through nodes + v2=nodes[(i + shift)%n] + G.add_edge(v1, v2) + return G + + +#------------------------------------------------------------------------------- +# Various small and named graphs +#------------------------------------------------------------------------------- + +def bull_graph(create_using=None): + """Return the Bull graph. """ + description=[ + "adjacencylist", + "Bull Graph", + 5, + [[2,3],[1,3,4],[1,2,5],[2],[3]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def chvatal_graph(create_using=None): + """Return the Chvátal graph.""" + description=[ + "adjacencylist", + "Chvatal Graph", + 12, + [[2,5,7,10],[3,6,8],[4,7,9],[5,8,10], + [6,9],[11,12],[11,12],[9,12], + [11],[11,12],[],[]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def cubical_graph(create_using=None): + """Return the 3-regular Platonic Cubical graph.""" + description=[ + "adjacencylist", + "Platonic Cubical Graph", + 8, + [[2,4,5],[1,3,8],[2,4,7],[1,3,6], + [1,6,8],[4,5,7],[3,6,8],[2,5,7]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def desargues_graph(create_using=None): + """ Return the Desargues graph.""" + G=LCF_graph(20, [5,-5,9,-9], 5, create_using) + G.name="Desargues Graph" + return G + +def diamond_graph(create_using=None): + """Return the Diamond graph. """ + description=[ + "adjacencylist", + "Diamond Graph", + 4, + [[2,3],[1,3,4],[1,2,4],[2,3]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def dodecahedral_graph(create_using=None): + """ Return the Platonic Dodecahedral graph. """ + G=LCF_graph(20, [10,7,4,-4,-7,10,-4,7,-7,4], 2, create_using) + G.name="Dodecahedral Graph" + return G + +def frucht_graph(create_using=None): + """Return the Frucht Graph. + + The Frucht Graph is the smallest cubical graph whose + automorphism group consists only of the identity element. + + """ + G=cycle_graph(7, create_using) + G.add_edges_from([[0,7],[1,7],[2,8],[3,9],[4,9],[5,10],[6,10], + [7,11],[8,11],[8,9],[10,11]]) + + G.name="Frucht Graph" + return G + +def heawood_graph(create_using=None): + """ Return the Heawood graph, a (3,6) cage. """ + G=LCF_graph(14, [5,-5], 7, create_using) + G.name="Heawood Graph" + return G + +def house_graph(create_using=None): + """Return the House graph (square with triangle on top).""" + description=[ + "adjacencylist", + "House Graph", + 5, + [[2,3],[1,4],[1,4,5],[2,3,5],[3,4]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def house_x_graph(create_using=None): + """Return the House graph with a cross inside the house square.""" + description=[ + "adjacencylist", + "House-with-X-inside Graph", + 5, + [[2,3,4],[1,3,4],[1,2,4,5],[1,2,3,5],[3,4]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def icosahedral_graph(create_using=None): + """Return the Platonic Icosahedral graph.""" + description=[ + "adjacencylist", + "Platonic Icosahedral Graph", + 12, + [[2,6,8,9,12],[3,6,7,9],[4,7,9,10],[5,7,10,11], + [6,7,11,12],[7,12],[],[9,10,11,12], + [10],[11],[12],[]] + ] + G=make_small_undirected_graph(description, create_using) + return G + + +def krackhardt_kite_graph(create_using=None): + """ + Return the Krackhardt Kite Social Network. + + A 10 actor social network introduced by David Krackhardt + to illustrate: degree, betweenness, centrality, closeness, etc. + The traditional labeling is: + Andre=1, Beverley=2, Carol=3, Diane=4, + Ed=5, Fernando=6, Garth=7, Heather=8, Ike=9, Jane=10. + + """ + description=[ + "adjacencylist", + "Krackhardt Kite Social Network", + 10, + [[2,3,4,6],[1,4,5,7],[1,4,6],[1,2,3,5,6,7],[2,4,7], + [1,3,4,7,8],[2,4,5,6,8],[6,7,9],[8,10],[9]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def moebius_kantor_graph(create_using=None): + """Return the Moebius-Kantor graph.""" + G=LCF_graph(16, [5,-5], 8, create_using) + G.name="Moebius-Kantor Graph" + return G + +def octahedral_graph(create_using=None): + """Return the Platonic Octahedral graph.""" + description=[ + "adjacencylist", + "Platonic Octahedral Graph", + 6, + [[2,3,4,5],[3,4,6],[5,6],[5,6],[6],[]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def pappus_graph(): + """ Return the Pappus graph.""" + G=LCF_graph(18,[5,7,-7,7,-7,-5],3) + G.name="Pappus Graph" + return G + +def petersen_graph(create_using=None): + """Return the Petersen graph.""" + description=[ + "adjacencylist", + "Petersen Graph", + 10, + [[2,5,6],[1,3,7],[2,4,8],[3,5,9],[4,1,10],[1,8,9],[2,9,10], + [3,6,10],[4,6,7],[5,7,8]] + ] + G=make_small_undirected_graph(description, create_using) + return G + + +def sedgewick_maze_graph(create_using=None): + """ + Return a small maze with a cycle. + + This is the maze used in Sedgewick,3rd Edition, Part 5, Graph + Algorithms, Chapter 18, e.g. Figure 18.2 and following. + Nodes are numbered 0,..,7 + """ + G=empty_graph(0, create_using) + G.add_nodes_from(range(8)) + G.add_edges_from([[0,2],[0,7],[0,5]]) + G.add_edges_from([[1,7],[2,6]]) + G.add_edges_from([[3,4],[3,5]]) + G.add_edges_from([[4,5],[4,7],[4,6]]) + G.name="Sedgewick Maze" + return G + +def tetrahedral_graph(create_using=None): + """ Return the 3-regular Platonic Tetrahedral graph.""" + G=complete_graph(4, create_using) + G.name="Platonic Tetrahedral graph" + return G + +def truncated_cube_graph(create_using=None): + """Return the skeleton of the truncated cube.""" + description=[ + "adjacencylist", + "Truncated Cube Graph", + 24, + [[2,3,5],[12,15],[4,5],[7,9], + [6],[17,19],[8,9],[11,13], + [10],[18,21],[12,13],[15], + [14],[22,23],[16],[20,24], + [18,19],[21],[20],[24], + [22],[23],[24],[]] + ] + G=make_small_undirected_graph(description, create_using) + return G + +def truncated_tetrahedron_graph(create_using=None): + """Return the skeleton of the truncated Platonic tetrahedron.""" + G=path_graph(12, create_using) +# G.add_edges_from([(1,3),(1,10),(2,7),(4,12),(5,12),(6,8),(9,11)]) + G.add_edges_from([(0,2),(0,9),(1,6),(3,11),(4,11),(5,7),(8,10)]) + G.name="Truncated Tetrahedron Graph" + return G + +def tutte_graph(create_using=None): + """Return the Tutte graph.""" + description=[ + "adjacencylist", + "Tutte's Graph", + 46, + [[2,3,4],[5,27],[11,12],[19,20],[6,34], + [7,30],[8,28],[9,15],[10,39],[11,38], + [40],[13,40],[14,36],[15,16],[35], + [17,23],[18,45],[19,44],[46],[21,46], + [22,42],[23,24],[41],[25,28],[26,33], + [27,32],[34],[29],[30,33],[31], + [32,34],[33],[],[],[36,39], + [37],[38,40],[39],[],[], + [42,45],[43],[44,46],[45],[],[]] + ] + G=make_small_undirected_graph(description, create_using) + return G + |