Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/link_analysis/hits_alg.py @ 0:4f3585e2f14b draft default tip
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author | shellac |
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date | Mon, 22 Mar 2021 18:12:50 +0000 |
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1 """Hubs and authorities analysis of graph structure. |
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2 """ |
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3 import networkx as nx |
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4 |
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5 __all__ = ["hits", "hits_numpy", "hits_scipy", "authority_matrix", "hub_matrix"] |
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6 |
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7 |
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8 def hits(G, max_iter=100, tol=1.0e-8, nstart=None, normalized=True): |
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9 """Returns HITS hubs and authorities values for nodes. |
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10 |
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11 The HITS algorithm computes two numbers for a node. |
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12 Authorities estimates the node value based on the incoming links. |
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13 Hubs estimates the node value based on outgoing links. |
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14 |
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15 Parameters |
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16 ---------- |
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17 G : graph |
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18 A NetworkX graph |
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19 |
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20 max_iter : integer, optional |
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21 Maximum number of iterations in power method. |
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22 |
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23 tol : float, optional |
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24 Error tolerance used to check convergence in power method iteration. |
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25 |
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26 nstart : dictionary, optional |
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27 Starting value of each node for power method iteration. |
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28 |
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29 normalized : bool (default=True) |
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30 Normalize results by the sum of all of the values. |
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31 |
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32 Returns |
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33 ------- |
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34 (hubs,authorities) : two-tuple of dictionaries |
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35 Two dictionaries keyed by node containing the hub and authority |
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36 values. |
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37 |
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38 Raises |
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39 ------ |
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40 PowerIterationFailedConvergence |
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41 If the algorithm fails to converge to the specified tolerance |
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42 within the specified number of iterations of the power iteration |
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43 method. |
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44 |
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45 Examples |
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46 -------- |
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47 >>> G = nx.path_graph(4) |
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48 >>> h, a = nx.hits(G) |
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49 |
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50 Notes |
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51 ----- |
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52 The eigenvector calculation is done by the power iteration method |
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53 and has no guarantee of convergence. The iteration will stop |
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54 after max_iter iterations or an error tolerance of |
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55 number_of_nodes(G)*tol has been reached. |
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56 |
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57 The HITS algorithm was designed for directed graphs but this |
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58 algorithm does not check if the input graph is directed and will |
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59 execute on undirected graphs. |
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60 |
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61 References |
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62 ---------- |
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63 .. [1] A. Langville and C. Meyer, |
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64 "A survey of eigenvector methods of web information retrieval." |
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65 http://citeseer.ist.psu.edu/713792.html |
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66 .. [2] Jon Kleinberg, |
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67 Authoritative sources in a hyperlinked environment |
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68 Journal of the ACM 46 (5): 604-32, 1999. |
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69 doi:10.1145/324133.324140. |
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70 http://www.cs.cornell.edu/home/kleinber/auth.pdf. |
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71 """ |
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72 if type(G) == nx.MultiGraph or type(G) == nx.MultiDiGraph: |
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73 raise Exception("hits() not defined for graphs with multiedges.") |
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74 if len(G) == 0: |
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75 return {}, {} |
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76 # choose fixed starting vector if not given |
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77 if nstart is None: |
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78 h = dict.fromkeys(G, 1.0 / G.number_of_nodes()) |
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79 else: |
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80 h = nstart |
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81 # normalize starting vector |
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82 s = 1.0 / sum(h.values()) |
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83 for k in h: |
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84 h[k] *= s |
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85 for _ in range(max_iter): # power iteration: make up to max_iter iterations |
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86 hlast = h |
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87 h = dict.fromkeys(hlast.keys(), 0) |
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88 a = dict.fromkeys(hlast.keys(), 0) |
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89 # this "matrix multiply" looks odd because it is |
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90 # doing a left multiply a^T=hlast^T*G |
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91 for n in h: |
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92 for nbr in G[n]: |
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93 a[nbr] += hlast[n] * G[n][nbr].get("weight", 1) |
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94 # now multiply h=Ga |
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95 for n in h: |
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96 for nbr in G[n]: |
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97 h[n] += a[nbr] * G[n][nbr].get("weight", 1) |
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98 # normalize vector |
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99 s = 1.0 / max(h.values()) |
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100 for n in h: |
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101 h[n] *= s |
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102 # normalize vector |
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103 s = 1.0 / max(a.values()) |
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104 for n in a: |
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105 a[n] *= s |
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106 # check convergence, l1 norm |
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107 err = sum([abs(h[n] - hlast[n]) for n in h]) |
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108 if err < tol: |
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109 break |
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110 else: |
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111 raise nx.PowerIterationFailedConvergence(max_iter) |
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112 if normalized: |
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113 s = 1.0 / sum(a.values()) |
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114 for n in a: |
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115 a[n] *= s |
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116 s = 1.0 / sum(h.values()) |
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117 for n in h: |
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118 h[n] *= s |
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119 return h, a |
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120 |
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121 |
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122 def authority_matrix(G, nodelist=None): |
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123 """Returns the HITS authority matrix.""" |
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124 M = nx.to_numpy_array(G, nodelist=nodelist) |
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125 return M.T @ M |
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126 |
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127 |
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128 def hub_matrix(G, nodelist=None): |
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129 """Returns the HITS hub matrix.""" |
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130 M = nx.to_numpy_array(G, nodelist=nodelist) |
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131 return M @ M.T |
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132 |
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133 |
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134 def hits_numpy(G, normalized=True): |
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135 """Returns HITS hubs and authorities values for nodes. |
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136 |
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137 The HITS algorithm computes two numbers for a node. |
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138 Authorities estimates the node value based on the incoming links. |
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139 Hubs estimates the node value based on outgoing links. |
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140 |
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141 Parameters |
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142 ---------- |
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143 G : graph |
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144 A NetworkX graph |
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145 |
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146 normalized : bool (default=True) |
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147 Normalize results by the sum of all of the values. |
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148 |
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149 Returns |
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150 ------- |
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151 (hubs,authorities) : two-tuple of dictionaries |
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152 Two dictionaries keyed by node containing the hub and authority |
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153 values. |
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154 |
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155 Examples |
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156 -------- |
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157 >>> G = nx.path_graph(4) |
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158 >>> h, a = nx.hits(G) |
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159 |
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160 Notes |
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161 ----- |
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162 The eigenvector calculation uses NumPy's interface to LAPACK. |
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163 |
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164 The HITS algorithm was designed for directed graphs but this |
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165 algorithm does not check if the input graph is directed and will |
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166 execute on undirected graphs. |
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167 |
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168 References |
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169 ---------- |
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170 .. [1] A. Langville and C. Meyer, |
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171 "A survey of eigenvector methods of web information retrieval." |
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172 http://citeseer.ist.psu.edu/713792.html |
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173 .. [2] Jon Kleinberg, |
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174 Authoritative sources in a hyperlinked environment |
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175 Journal of the ACM 46 (5): 604-32, 1999. |
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176 doi:10.1145/324133.324140. |
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177 http://www.cs.cornell.edu/home/kleinber/auth.pdf. |
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178 """ |
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179 try: |
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180 import numpy as np |
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181 except ImportError as e: |
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182 raise ImportError("hits_numpy() requires NumPy: " "http://numpy.org/") from e |
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183 if len(G) == 0: |
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184 return {}, {} |
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185 H = nx.hub_matrix(G, list(G)) |
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186 e, ev = np.linalg.eig(H) |
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187 m = e.argsort()[-1] # index of maximum eigenvalue |
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188 h = np.array(ev[:, m]).flatten() |
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189 A = nx.authority_matrix(G, list(G)) |
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190 e, ev = np.linalg.eig(A) |
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191 m = e.argsort()[-1] # index of maximum eigenvalue |
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192 a = np.array(ev[:, m]).flatten() |
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193 if normalized: |
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194 h = h / h.sum() |
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195 a = a / a.sum() |
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196 else: |
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197 h = h / h.max() |
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198 a = a / a.max() |
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199 hubs = dict(zip(G, map(float, h))) |
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200 authorities = dict(zip(G, map(float, a))) |
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201 return hubs, authorities |
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202 |
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203 |
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204 def hits_scipy(G, max_iter=100, tol=1.0e-6, normalized=True): |
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205 """Returns HITS hubs and authorities values for nodes. |
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206 |
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207 The HITS algorithm computes two numbers for a node. |
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208 Authorities estimates the node value based on the incoming links. |
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209 Hubs estimates the node value based on outgoing links. |
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210 |
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211 Parameters |
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212 ---------- |
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213 G : graph |
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214 A NetworkX graph |
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215 |
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216 max_iter : integer, optional |
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217 Maximum number of iterations in power method. |
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218 |
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219 tol : float, optional |
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220 Error tolerance used to check convergence in power method iteration. |
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221 |
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222 nstart : dictionary, optional |
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223 Starting value of each node for power method iteration. |
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224 |
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225 normalized : bool (default=True) |
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226 Normalize results by the sum of all of the values. |
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227 |
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228 Returns |
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229 ------- |
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230 (hubs,authorities) : two-tuple of dictionaries |
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231 Two dictionaries keyed by node containing the hub and authority |
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232 values. |
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233 |
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234 Examples |
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235 -------- |
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236 >>> G = nx.path_graph(4) |
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237 >>> h, a = nx.hits(G) |
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238 |
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239 Notes |
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240 ----- |
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241 This implementation uses SciPy sparse matrices. |
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242 |
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243 The eigenvector calculation is done by the power iteration method |
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244 and has no guarantee of convergence. The iteration will stop |
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245 after max_iter iterations or an error tolerance of |
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246 number_of_nodes(G)*tol has been reached. |
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247 |
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248 The HITS algorithm was designed for directed graphs but this |
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249 algorithm does not check if the input graph is directed and will |
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250 execute on undirected graphs. |
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251 |
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252 Raises |
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253 ------ |
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254 PowerIterationFailedConvergence |
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255 If the algorithm fails to converge to the specified tolerance |
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256 within the specified number of iterations of the power iteration |
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257 method. |
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258 |
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259 References |
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260 ---------- |
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261 .. [1] A. Langville and C. Meyer, |
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262 "A survey of eigenvector methods of web information retrieval." |
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263 http://citeseer.ist.psu.edu/713792.html |
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264 .. [2] Jon Kleinberg, |
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265 Authoritative sources in a hyperlinked environment |
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266 Journal of the ACM 46 (5): 604-632, 1999. |
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267 doi:10.1145/324133.324140. |
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268 http://www.cs.cornell.edu/home/kleinber/auth.pdf. |
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269 """ |
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270 try: |
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271 import numpy as np |
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272 except ImportError as e: |
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273 raise ImportError( |
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274 "hits_scipy() requires SciPy and NumPy:" |
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275 "http://scipy.org/ http://numpy.org/" |
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276 ) from e |
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277 if len(G) == 0: |
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278 return {}, {} |
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279 M = nx.to_scipy_sparse_matrix(G, nodelist=list(G)) |
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280 (n, m) = M.shape # should be square |
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281 A = M.T * M # authority matrix |
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282 x = np.ones((n, 1)) / n # initial guess |
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283 # power iteration on authority matrix |
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284 i = 0 |
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285 while True: |
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286 xlast = x |
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287 x = A * x |
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288 x = x / x.max() |
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289 # check convergence, l1 norm |
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290 err = np.absolute(x - xlast).sum() |
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291 if err < tol: |
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292 break |
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293 if i > max_iter: |
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294 raise nx.PowerIterationFailedConvergence(max_iter) |
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295 i += 1 |
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296 |
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297 a = np.asarray(x).flatten() |
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298 # h=M*a |
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299 h = np.asarray(M * a).flatten() |
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300 if normalized: |
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301 h = h / h.sum() |
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302 a = a / a.sum() |
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303 hubs = dict(zip(G, map(float, h))) |
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304 authorities = dict(zip(G, map(float, a))) |
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305 return hubs, authorities |