Mercurial > repos > shellac > sam_consensus_v3
annotate env/lib/python3.9/site-packages/networkx/algorithms/assortativity/neighbor_degree.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 __all__ = ["average_neighbor_degree"] |
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2 |
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3 |
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4 def _average_nbr_deg(G, source_degree, target_degree, nodes=None, weight=None): |
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5 # average degree of neighbors |
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6 avg = {} |
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7 for n, deg in source_degree(nodes, weight=weight): |
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8 # normalize but not by zero degree |
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9 if deg == 0: |
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10 deg = 1 |
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11 nbrdeg = target_degree(G[n]) |
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12 if weight is None: |
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13 avg[n] = sum(d for n, d in nbrdeg) / float(deg) |
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14 else: |
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15 avg[n] = sum((G[n][nbr].get(weight, 1) * d for nbr, d in nbrdeg)) / float( |
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16 deg |
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17 ) |
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18 return avg |
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19 |
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20 |
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21 def average_neighbor_degree(G, source="out", target="out", nodes=None, weight=None): |
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22 r"""Returns the average degree of the neighborhood of each node. |
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23 |
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24 The average neighborhood degree of a node `i` is |
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25 |
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26 .. math:: |
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27 |
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28 k_{nn,i} = \frac{1}{|N(i)|} \sum_{j \in N(i)} k_j |
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29 |
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30 where `N(i)` are the neighbors of node `i` and `k_j` is |
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31 the degree of node `j` which belongs to `N(i)`. For weighted |
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32 graphs, an analogous measure can be defined [1]_, |
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33 |
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34 .. math:: |
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35 |
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36 k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j |
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37 |
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38 where `s_i` is the weighted degree of node `i`, `w_{ij}` |
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39 is the weight of the edge that links `i` and `j` and |
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40 `N(i)` are the neighbors of node `i`. |
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41 |
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42 |
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43 Parameters |
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44 ---------- |
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45 G : NetworkX graph |
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46 |
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47 source : string ("in"|"out") |
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48 Directed graphs only. |
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49 Use "in"- or "out"-degree for source node. |
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50 |
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51 target : string ("in"|"out") |
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52 Directed graphs only. |
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53 Use "in"- or "out"-degree for target node. |
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54 |
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55 nodes : list or iterable, optional |
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56 Compute neighbor degree for specified nodes. The default is |
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57 all nodes in the graph. |
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58 |
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59 weight : string or None, optional (default=None) |
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60 The edge attribute that holds the numerical value used as a weight. |
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61 If None, then each edge has weight 1. |
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62 |
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63 Returns |
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64 ------- |
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65 d: dict |
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66 A dictionary keyed by node with average neighbors degree value. |
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67 |
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68 Examples |
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69 -------- |
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70 >>> G = nx.path_graph(4) |
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71 >>> G.edges[0, 1]["weight"] = 5 |
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72 >>> G.edges[2, 3]["weight"] = 3 |
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73 |
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74 >>> nx.average_neighbor_degree(G) |
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75 {0: 2.0, 1: 1.5, 2: 1.5, 3: 2.0} |
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76 >>> nx.average_neighbor_degree(G, weight="weight") |
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77 {0: 2.0, 1: 1.1666666666666667, 2: 1.25, 3: 2.0} |
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78 |
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79 >>> G = nx.DiGraph() |
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80 >>> nx.add_path(G, [0, 1, 2, 3]) |
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81 >>> nx.average_neighbor_degree(G, source="in", target="in") |
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82 {0: 1.0, 1: 1.0, 2: 1.0, 3: 0.0} |
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83 |
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84 >>> nx.average_neighbor_degree(G, source="out", target="out") |
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85 {0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0} |
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86 |
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87 Notes |
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88 ----- |
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89 For directed graphs you can also specify in-degree or out-degree |
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90 by passing keyword arguments. |
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91 |
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92 See Also |
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93 -------- |
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94 average_degree_connectivity |
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95 |
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96 References |
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97 ---------- |
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98 .. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, |
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99 "The architecture of complex weighted networks". |
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100 PNAS 101 (11): 3747–3752 (2004). |
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101 """ |
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102 source_degree = G.degree |
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103 target_degree = G.degree |
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104 if G.is_directed(): |
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105 direction = {"out": G.out_degree, "in": G.in_degree} |
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106 source_degree = direction[source] |
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107 target_degree = direction[target] |
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108 return _average_nbr_deg(G, source_degree, target_degree, nodes=nodes, weight=weight) |
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109 |
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110 |
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111 # obsolete |
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112 # def average_neighbor_in_degree(G, nodes=None, weight=None): |
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113 # if not G.is_directed(): |
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114 # raise nx.NetworkXError("Not defined for undirected graphs.") |
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115 # return _average_nbr_deg(G, G.in_degree, G.in_degree, nodes, weight) |
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116 # average_neighbor_in_degree.__doc__=average_neighbor_degree.__doc__ |
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117 |
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118 # def average_neighbor_out_degree(G, nodes=None, weight=None): |
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119 # if not G.is_directed(): |
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120 # raise nx.NetworkXError("Not defined for undirected graphs.") |
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121 # return _average_nbr_deg(G, G.out_degree, G.out_degree, nodes, weight) |
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122 # average_neighbor_out_degree.__doc__=average_neighbor_degree.__doc__ |