Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/centrality/trophic.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 """Trophic levels""" |
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2 import networkx as nx |
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3 |
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4 from networkx.utils import not_implemented_for |
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5 |
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6 __all__ = ["trophic_levels", "trophic_differences", "trophic_incoherence_parameter"] |
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7 |
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8 |
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9 @not_implemented_for("undirected") |
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10 def trophic_levels(G, weight="weight"): |
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11 r"""Compute the trophic levels of nodes. |
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12 |
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13 The trophic level of a node $i$ is |
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14 |
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15 .. math:: |
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16 |
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17 s_i = 1 + \frac{1}{k^{in}_i} \sum_{j} a_{ij} s_j |
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18 |
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19 where $k^{in}_i$ is the in-degree of i |
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20 |
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21 .. math:: |
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22 |
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23 k^{in}_i = \sum_{j} a_{ij} |
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24 |
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25 and nodes with $k^{in}_i = 0$ have $s_i = 1$ by convention. |
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26 |
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27 These are calculated using the method outlined in Levine [1]_. |
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28 |
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29 Parameters |
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30 ---------- |
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31 G : DiGraph |
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32 A directed networkx graph |
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33 |
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34 Returns |
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35 ------- |
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36 nodes : dict |
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37 Dictionary of nodes with trophic level as the vale. |
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38 |
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39 References |
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40 ---------- |
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41 .. [1] Stephen Levine (1980) J. theor. Biol. 83, 195-207 |
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42 """ |
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43 try: |
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44 import numpy as np |
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45 except ImportError as e: |
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46 raise ImportError("trophic_levels() requires NumPy: http://numpy.org/") from e |
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47 |
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48 # find adjacency matrix |
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49 a = nx.adjacency_matrix(G, weight=weight).T.toarray() |
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50 |
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51 # drop rows/columns where in-degree is zero |
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52 rowsum = np.sum(a, axis=1) |
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53 p = a[rowsum != 0][:, rowsum != 0] |
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54 # normalise so sum of in-degree weights is 1 along each row |
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55 p = p / rowsum[rowsum != 0][:, np.newaxis] |
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56 |
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57 # calculate trophic levels |
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58 nn = p.shape[0] |
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59 i = np.eye(nn) |
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60 try: |
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61 n = np.linalg.inv(i - p) |
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62 except np.linalg.LinAlgError as err: |
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63 # LinAlgError is raised when there is a non-basal node |
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64 msg = ( |
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65 "Trophic levels are only defined for graphs where every " |
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66 + "node has a path from a basal node (basal nodes are nodes " |
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67 + "with no incoming edges)." |
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68 ) |
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69 raise nx.NetworkXError(msg) from err |
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70 y = n.sum(axis=1) + 1 |
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71 |
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72 levels = {} |
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73 |
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74 # all nodes with in-degree zero have trophic level == 1 |
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75 zero_node_ids = (node_id for node_id, degree in G.in_degree if degree == 0) |
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76 for node_id in zero_node_ids: |
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77 levels[node_id] = 1 |
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78 |
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79 # all other nodes have levels as calculated |
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80 nonzero_node_ids = (node_id for node_id, degree in G.in_degree if degree != 0) |
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81 for i, node_id in enumerate(nonzero_node_ids): |
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82 levels[node_id] = y[i] |
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83 |
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84 return levels |
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85 |
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86 |
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87 @not_implemented_for("undirected") |
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88 def trophic_differences(G, weight="weight"): |
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89 r"""Compute the trophic differences of the edges of a directed graph. |
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90 |
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91 The trophic difference $x_ij$ for each edge is defined in Johnson et al. |
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92 [1]_ as: |
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93 |
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94 .. math:: |
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95 x_ij = s_j - s_i |
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96 |
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97 Where $s_i$ is the trophic level of node $i$. |
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98 |
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99 Parameters |
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100 ---------- |
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101 G : DiGraph |
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102 A directed networkx graph |
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103 |
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104 Returns |
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105 ------- |
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106 diffs : dict |
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107 Dictionary of edges with trophic differences as the value. |
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108 |
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109 References |
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110 ---------- |
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111 .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. |
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112 Munoz (2014) PNAS "Trophic coherence determines food-web stability" |
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113 """ |
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114 levels = trophic_levels(G, weight=weight) |
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115 diffs = {} |
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116 for u, v in G.edges: |
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117 diffs[(u, v)] = levels[v] - levels[u] |
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118 return diffs |
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119 |
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120 |
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121 @not_implemented_for("undirected") |
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122 def trophic_incoherence_parameter(G, weight="weight", cannibalism=False): |
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123 r"""Compute the trophic incoherence parameter of a graph. |
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124 |
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125 Trophic coherence is defined as the homogeneity of the distribution of |
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126 trophic distances: the more similar, the more coherent. This is measured by |
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127 the standard deviation of the trophic differences and referred to as the |
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128 trophic incoherence parameter $q$ by [1]. |
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129 |
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130 Parameters |
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131 ---------- |
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132 G : DiGraph |
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133 A directed networkx graph |
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134 |
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135 cannibalism: Boolean |
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136 If set to False, self edges are not considered in the calculation |
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137 |
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138 Returns |
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139 ------- |
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140 trophic_incoherence_parameter : float |
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141 The trophic coherence of a graph |
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142 |
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143 References |
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144 ---------- |
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145 .. [1] Samuel Johnson, Virginia Dominguez-Garcia, Luca Donetti, Miguel A. |
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146 Munoz (2014) PNAS "Trophic coherence determines food-web stability" |
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147 """ |
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148 try: |
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149 import numpy as np |
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150 except ImportError as e: |
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151 raise ImportError( |
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152 "trophic_incoherence_parameter() requires NumPy: " "http://scipy.org/" |
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153 ) from e |
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154 |
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155 if cannibalism: |
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156 diffs = trophic_differences(G, weight=weight) |
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157 else: |
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158 # If no cannibalism, remove self-edges |
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159 self_loops = list(nx.selfloop_edges(G)) |
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160 if self_loops: |
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161 # Make a copy so we do not change G's edges in memory |
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162 G_2 = G.copy() |
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163 G_2.remove_edges_from(self_loops) |
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164 else: |
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165 # Avoid copy otherwise |
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166 G_2 = G |
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167 diffs = trophic_differences(G_2, weight=weight) |
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168 return np.std(list(diffs.values())) |