Python图算法实例分析

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
#encoding=utf-8
import networkx,heapq,sys
from matplotlib import pyplot
from collections import defaultdict,OrderedDict
from numpy import array
# Data in graphdata.txt:
# a b  4
# a h  8
# b c  8
# b h  11
# h i  7
# h g  1
# g i  6
# g f  2
# c f  4
# c i  2
# c d  7
# d f  14
# d e  9
# f e  10
def Edge(): return defaultdict(Edge)
class Graph:
  def __init__(self):
    self.Link = Edge()
    self.FileName = ''
    self.Separator = ''
  def MakeLink(self,filename,separator):
    self.FileName = filename
    self.Separator = separator
    graphfile = open(filename,'r')
    for line in graphfile:
      items = line.split(separator)
      self.Link[items[0]][items[1]] = int(items[2])
      self.Link[items[1]][items[0]] = int(items[2])
    graphfile.close()
  def LocalClusteringCoefficient(self,node):
    neighbors = self.Link[node]
    if len(neighbors) <= 1: return 0
    links = 0
    for j in neighbors:
      for k in neighbors:
        if j in self.Link[k]:
          links += 0.5
    return 2.0*links/(len(neighbors)*(len(neighbors)-1))
  def AverageClusteringCoefficient(self):
    total = 0.0
    for node in self.Link.keys():
      total += self.LocalClusteringCoefficient(node)
    return total/len(self.Link.keys())
  def DeepFirstSearch(self,start):
    visitedNodes = []
    todoList = [start]
    while todoList:
      visit = todoList.pop(0)
      if visit not in visitedNodes:
        visitedNodes.append(visit)
        todoList = self.Link[visit].keys() + todoList
    return visitedNodes
  def BreadthFirstSearch(self,start):
    visitedNodes = []
    todoList = [start]
    while todoList:
      visit = todoList.pop(0)
      if visit not in visitedNodes:
        visitedNodes.append(visit)
        todoList = todoList + self.Link[visit].keys()
    return visitedNodes
  def ListAllComponent(self):
    allComponent = []
    visited = {}
    for node in self.Link.iterkeys():
      if node not in visited:
        oneComponent = self.MakeComponent(node,visited)
        allComponent.append(oneComponent)
    return allComponent
  def CheckConnection(self,node1,node2):
    return True if node2 in self.MakeComponent(node1,{}) else False
  def MakeComponent(self,node,visited):
    visited[node] = True
    component = [node]
    for neighbor in self.Link[node]:
      if neighbor not in visited:
        component += self.MakeComponent(neighbor,visited)
    return component
  def MinimumSpanningTree_Kruskal(self,start):
    graphEdges = [line.strip('\n').split(self.Separator) for line in open(self.FileName,'r')]
    nodeSet = {}
    for idx,node in enumerate(self.MakeComponent(start,{})):
      nodeSet[node] = idx
    edgeNumber = 0; totalEdgeNumber = len(nodeSet)-1
    for oneEdge in sorted(graphEdges,key=lambda x:int(x[2]),reverse=False):
      if edgeNumber == totalEdgeNumber: break
      nodeA,nodeB,cost = oneEdge
      if nodeA in nodeSet and nodeSet[nodeA] != nodeSet[nodeB]:
        nodeBSet = nodeSet[nodeB]
        for node in nodeSet.keys():
          if nodeSet[node] == nodeBSet:
            nodeSet[node] = nodeSet[nodeA]
        print nodeA,nodeB,cost
        edgeNumber += 1
  def MinimumSpanningTree_Prim(self,start):
    expandNode = set(self.MakeComponent(start,{}))
    distFromTreeSoFar = {}.fromkeys(expandNode,sys.maxint); distFromTreeSoFar[start] = 0
    linkToNode = {}.fromkeys(expandNode,'');linkToNode[start] = start
    while expandNode:
      # Find the closest dist node
      closestNode = ''; shortestdistance = sys.maxint;
      for node,dist in distFromTreeSoFar.iteritems():
        if node in expandNode and dist < shortestdistance:
          closestNode,shortestdistance = node,dist
      expandNode.remove(closestNode)
      print linkToNode[closestNode],closestNode,shortestdistance
      for neighbor in self.Link[closestNode].iterkeys():
        recomputedist = self.Link[closestNode][neighbor]
        if recomputedist < distFromTreeSoFar[neighbor]:
          distFromTreeSoFar[neighbor] = recomputedist
          linkToNode[neighbor] = closestNode
  def ShortestPathOne2One(self,start,end):
    pathFromStart = {}
    pathFromStart[start] = [start]
    todoList = [start]
    while todoList:
      current = todoList.pop(0)
      for neighbor in self.Link[current]:
        if neighbor not in pathFromStart:
          pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
          if neighbor == end:
            return pathFromStart[end]
          todoList.append(neighbor)
    return []
  def Centrality(self,node):
    path2All = self.ShortestPathOne2All(node)
    # The average of the distances of all the reachable nodes
    return float(sum([len(path)-1 for path in path2All.itervalues()]))/len(path2All)
  def SingleSourceShortestPath_Dijkstra(self,start):
    expandNode = set(self.MakeComponent(start,{}))
    distFromSourceSoFar = {}.fromkeys(expandNode,sys.maxint); distFromSourceSoFar[start] = 0
    while expandNode:
      # Find the closest dist node
      closestNode = ''; shortestdistance = sys.maxint;
      for node,dist in distFromSourceSoFar.iteritems():
        if node in expandNode and dist < shortestdistance:
          closestNode,shortestdistance = node,dist
      expandNode.remove(closestNode)
      for neighbor in self.Link[closestNode].iterkeys():
        recomputedist = distFromSourceSoFar[closestNode] + self.Link[closestNode][neighbor]
        if recomputedist < distFromSourceSoFar[neighbor]:
          distFromSourceSoFar[neighbor] = recomputedist
    for node in distFromSourceSoFar:
      print start,node,distFromSourceSoFar[node]
  def AllpairsShortestPaths_MatrixMultiplication(self,start):
    nodeIdx = {}; idxNode = {}; 
    for idx,node in enumerate(self.MakeComponent(start,{})):
      nodeIdx[node] = idx; idxNode[idx] = node
    matrixSize = len(nodeIdx)
    MaxInt = 1000
    nodeMatrix = array([[MaxInt]*matrixSize]*matrixSize)
    for node in nodeIdx.iterkeys():
      nodeMatrix[nodeIdx[node]][nodeIdx[node]] = 0
    for line in open(self.FileName,'r'):
      nodeA,nodeB,cost = line.strip('\n').split(self.Separator)
      if nodeA in nodeIdx:
        nodeMatrix[nodeIdx[nodeA]][nodeIdx[nodeB]] = int(cost)
        nodeMatrix[nodeIdx[nodeB]][nodeIdx[nodeA]] = int(cost)
    result = array([[0]*matrixSize]*matrixSize)
    for i in xrange(matrixSize):
      for j in xrange(matrixSize):
        result[i][j] = nodeMatrix[i][j]
    for itertime in xrange(2,matrixSize):
      for i in xrange(matrixSize):
        for j in xrange(matrixSize):
          if i==j:
            result[i][j] = 0
            continue
          result[i][j] = MaxInt
          for k in xrange(matrixSize):
            result[i][j] = min(result[i][j],result[i][k]+nodeMatrix[k][j])
    for i in xrange(matrixSize):
      for j in xrange(matrixSize):
        if result[i][j] != MaxInt:
          print idxNode[i],idxNode[j],result[i][j]
  def ShortestPathOne2All(self,start):
    pathFromStart = {}
    pathFromStart[start] = [start]
    todoList = [start]
    while todoList:
      current = todoList.pop(0)
      for neighbor in self.Link[current]:
        if neighbor not in pathFromStart:
          pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
          todoList.append(neighbor)
    return pathFromStart
  def NDegreeNode(self,start,n):
    pathFromStart = {}
    pathFromStart[start] = [start]
    pathLenFromStart = {}
    pathLenFromStart[start] = 0
    todoList = [start]
    while todoList:
      current = todoList.pop(0)
      for neighbor in self.Link[current]:
        if neighbor not in pathFromStart:
          pathFromStart[neighbor] = pathFromStart[current] + [neighbor]
          pathLenFromStart[neighbor] = pathLenFromStart[current] + 1
          if pathLenFromStart[neighbor] <= n+1:
            todoList.append(neighbor)
    for node in pathFromStart.keys():
      if len(pathFromStart[node]) != n+1:
        del pathFromStart[node]
    return pathFromStart
  def Draw(self):
    G = networkx.Graph()
    nodes = self.Link.keys()
    edges = [(node,neighbor) for node in nodes for neighbor in self.Link[node]]
    G.add_edges_from(edges)
    networkx.draw(G)
    pyplot.show()
if __name__=='__main__':
  separator = '\t'
  filename = 'C:\\Users\\Administrator\\Desktop\\graphdata.txt'
  resultfilename = 'C:\\Users\\Administrator\\Desktop\\result.txt'
  myGraph = Graph()
  myGraph.MakeLink(filename,separator)
  print 'LocalClusteringCoefficient',myGraph.LocalClusteringCoefficient('a')
  print 'AverageClusteringCoefficient',myGraph.AverageClusteringCoefficient()
  print 'DeepFirstSearch',myGraph.DeepFirstSearch('a')
  print 'BreadthFirstSearch',myGraph.BreadthFirstSearch('a')
  print 'ShortestPathOne2One',myGraph.ShortestPathOne2One('a','d')
  print 'ShortestPathOne2All',myGraph.ShortestPathOne2All('a')
  print 'NDegreeNode',myGraph.NDegreeNode('a',3).keys()
  print 'ListAllComponent',myGraph.ListAllComponent()
  print 'CheckConnection',myGraph.CheckConnection('a','f')
  print 'Centrality',myGraph.Centrality('c')
  myGraph.MinimumSpanningTree_Kruskal('a')
  myGraph.AllpairsShortestPaths_MatrixMultiplication('a')
  myGraph.MinimumSpanningTree_Prim('a')
  myGraph.SingleSourceShortestPath_Dijkstra('a')
  # myGraph.Draw()