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1 """ Code example from Complexity and Computation, a book about
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2 exploring complexity science with Python. Available free from
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3
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4 http://greenteapress.com/complexity
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5
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6 Copyright 2011 Allen B. Downey.
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7 Distributed under the GNU General Public License at gnu.org/licenses/gpl.html.
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8 """
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9 import itertools
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10 from collections import deque
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11
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12
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13 class GraphError(Exception):
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14 """Exception for Graph errors"""
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15 pass
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16
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17
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18 class Vertex(object):
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19 """A Vertex is a node in a graph."""
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20
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21 def __init__(self, label=''):
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22 self.label = label
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23
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24 def __repr__(self):
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25 """Returns a string representation of this object that can
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26 be evaluated as a Python expression."""
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27 return 'Vertex(%s)' % repr(self.label)
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28
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29 __str__ = __repr__
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30 """The str and repr forms of this object are the same."""
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31
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32
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33 class Edge(tuple):
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34 """An Edge is a list of two vertices."""
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35
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36 def __new__(cls, *vs):
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37 """The Edge constructor takes two vertices."""
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38 if len(vs) != 2:
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39 raise ValueError, 'Edges must connect exactly two vertices.'
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40 return tuple.__new__(cls, vs)
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41
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42 def __repr__(self):
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43 """Return a string representation of this object that can
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44 be evaluated as a Python expression."""
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45 return 'Edge(%s, %s)' % (repr(self[0]), repr(self[1]))
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46
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47 __str__ = __repr__
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48 """The str and repr forms of this object are the same."""
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49
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50
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51 class Graph(dict):
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52 """A Graph is a dictionary of dictionaries. The outer
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53 dictionary maps from a vertex to an inner dictionary.
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54 The inner dictionary maps from other vertices to edges.
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55
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56 For vertices a and b, graph[a][b] maps
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57 to the edge that connects a->b, if it exists."""
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58
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59 def __init__(self, vs=None, es=None):
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60 """Creates a new graph.
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61 vs: list of vertices;
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62 es: list of edges.
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63 """
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64 if vs:
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65 for v in vs:
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66 self.add_vertex(v)
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67
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68 if es:
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69 for e in es:
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70 self.add_edge(e)
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71
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72 def add_vertex(self, v):
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73 """Add a vertex to the graph."""
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74 self[v] = {}
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75
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76 def add_edge(self, e):
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77 """Adds and edge to the graph by adding an entry in both directions.
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78
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79 If there is already an edge connecting these Vertices, the
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80 new edge replaces it.
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81 """
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82 v, w = e
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83 self[v][w] = e
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84 self[w][v] = e
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85
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86 def get_edge(self, v, w):
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87 """Returns the edge object that exists between the two vertices v & w,
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88 or None if no such edge exists.
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89
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90 """
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91 try:
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92 return self[v][w]
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93 except KeyError:
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94 return None
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95
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96 def remove_edge(self, e):
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97 """Removes the edge e from the graph."""
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98
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99 v, w = e
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100 del self[v][w]
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101 del self[w][v]
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102
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103 def vertices(self):
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104 """Returns a list of the vertices in the graph."""
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105
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106 return self.keys()
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107
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108 def edges(self):
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109 """"Returns a list of the edges in the graph."""
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110
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111 edge_set = set()
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112 for d in self.itervalues():
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113 edge_set.update(d.itervalues())
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114
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115 return list(edge_set)
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116
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117 def out_vertices(self, v):
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118 """Returns a list of vertices that are adjacent to the given vertex v.
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119
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120 """
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121 return self[v].keys()
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122
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123 def out_edges(self, v):
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124 """Returns a list of edges connected to a given vertex v."""
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125
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126 return self[v].values()
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127
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128 def remove_all_edges(self):
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129 """Removes all edges in the graph."""
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130 for v in self.iterkeys():
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131 self[v] = {}
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132
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133 def add_all_edges(self):
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134 """Makes the graph complete by adding edges between all pairs of
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135 vertices.
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136
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137 """
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138 # Clear all edges first
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139 self.remove_all_edges()
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140
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141 # For each combination of 2 vertices, create an edge between them:
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142 for v, w in itertools.combinations(self.iterkeys(), 2):
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143 self.add_edge(Edge(v, w))
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144
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145 def add_regular_edges(self, k):
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146 """Makes the graph regular by making every vertex have k edges.
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147
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148 It is not always possible to create a regular graph with a given degree.
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149 If a graph has n vertices, then a regular graph can be constructed with
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150 degree k if n >= k + 1 and n * k is even. If these conditions are not
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151 met a GraphError exception is raised.
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152
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153 """
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154 n = len(self.vertices())
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155 if n < k + 1:
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156 raise GraphError("Can't make a regular graph with degree >= number"
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157 " of vertices")
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158 if (n * k) % 2 != 0:
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159 raise GraphError("Can't make a regular graph of degree k and"
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160 " order n where k * n is odd")
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161
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162 # Remove all edges first
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163 self.remove_all_edges()
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164
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165 if k % 2 != 0: # if k is odd
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166 self._add_regular_edges_even(k - 1)
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167 self._add_regular_edges_odd()
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168 else:
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169 self._add_regular_edges_even(k)
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170
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171 def _add_regular_edges_even(self, k):
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172 """Make a regular graph with degree k. k must be even."""
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173
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174 vs = self.vertices()
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175 vs2 = vs * 2
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176
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177 for i, v in enumerate(vs):
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178 for j in range(1, k / 2 + 1):
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179 w = vs2[i + j]
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180 self.add_edge(Edge(v, w))
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181
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182 def _add_regular_edges_odd(self):
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183 """Adds an extra edge across the graph to finish off a regular graph
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184 with odd degree. The number of vertices must be even.
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185
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186 """
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187 vs = self.vertices()
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188 vs2 = vs * 2
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189 n = len(vs)
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190
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191 for i in range(n / 2):
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192 v = vs2[i]
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193 w = vs2[i + n / 2]
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194 self.add_edge(Edge(v, w))
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195
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196 def bfs(self, start, visit_func=None):
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197 """Perform a breadth first search starting at node start.
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198
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199 The function visit_func, if supplied, is invoked on each node.
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200
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201 The set of visited nodes is returned.
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202
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203 """
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204 visited = set()
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205
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206 # Create a work queue consisting initially of the starting node
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207 queue = deque([start])
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208
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209 while queue:
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210 # retrieve first item from the queue
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211 v = queue.popleft()
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212
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213 if v in visited:
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214 continue # Skip this one if we've seen it before
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215
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216 # Mark it as visited and invoke user's function on it
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217 visited.add(v)
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218 if visit_func:
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219 visit_func(v)
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220
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221 # Add the adjacent neigbors to the node to the queue
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222 queue.extend(c for c in self.out_vertices(v) if c not in visited)
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223
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224 return visited
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225
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226 def is_connected(self):
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227 """Returns True if the graph is connected (there is a path from every
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228 node to every other node) and False otherwise.
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229
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230 """
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231 vs = self.vertices()
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232 if len(vs):
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233 visited = self.bfs(vs[0])
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234 # See if all nodes have been visited
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235 return len(vs) == len(visited)
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236
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237 return False # Graph is empty
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238
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239
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bgneal@1
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240 def main(script, *args):
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241 import pprint
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242
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243 v = Vertex('v')
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244 print v
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245 w = Vertex('w')
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246 print w
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247 e = Edge(v, w)
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248 print e
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249 g = Graph([v,w], [e])
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250 pprint.pprint(g)
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251
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252 print "g.get_edge(v, w): ", g.get_edge(v, w)
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253 x = Vertex('x')
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254 print "g.get_edge(v, x): ", g.get_edge(v, x)
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255
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256 g.remove_edge(e)
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257 pprint.pprint(g)
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258
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259 print "vertices: ", g.vertices()
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260 print "edges: ", g.edges()
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261
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262 g.add_edge(e)
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263 u = Vertex('u')
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264 e1 = Edge(u, v)
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265 e2 = Edge(u, w)
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266 g.add_vertex(u)
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267 g.add_edge(e1)
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268 g.add_edge(e2)
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269 print "Adding vertex u and edges:"
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270 pprint.pprint(g)
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271 print "vertices: ", g.vertices()
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272 print "edges: ", g.edges()
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273
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274 print "Out vertices for v: ", g.out_vertices(v)
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bgneal@1
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275 print "Out edges for v: ", g.out_edges(v)
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276
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277 x = Vertex('x')
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278 g.add_vertex(x)
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279 g.add_all_edges()
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bgneal@1
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280 pprint.pprint(g)
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281
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bgneal@7
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282 print "g is connected?", g.is_connected()
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bgneal@7
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283 edges = g.out_edges(v)
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bgneal@7
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284 for e in edges:
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bgneal@7
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285 g.remove_edge(e)
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bgneal@7
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286 pprint.pprint(g)
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bgneal@7
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287 print "g is connected?", g.is_connected()
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bgneal@7
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288
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bgneal@7
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289 # Isolate v and check is_connected() again
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290
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bgneal@1
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291
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bgneal@1
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292 if __name__ == '__main__':
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bgneal@1
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293 import sys
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bgneal@1
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294 main(*sys.argv)
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