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# Copyright (C) 2011 by
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# Jordi Torrents <jtorrents@milnou.net>
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# Aric Hagberg <hagberg@lanl.gov>
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__author__ = """\n""".join(['Jordi Torrents <jtorrents@milnou.net>',
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'Aric Hagberg (hagberg@lanl.gov)'])
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__all__ = ["average_neighbor_degree"]
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def _average_nbr_deg(G, source_degree, target_degree, nodes=None, weight=None):
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# average degree of neighbors
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for n,deg in source_degree(nodes,weight=weight).items():
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# normalize but not by zero degree
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nbrdeg = target_degree(G[n])
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avg[n] = sum(nbrdeg.values())/float(deg)
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avg[n] = sum((G[n][nbr].get(weight,1)*d
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for nbr,d in nbrdeg.items()))/float(deg)
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def average_neighbor_degree(G, source='out', target='out',
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nodes=None, weight=None):
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r"""Returns the average degree of the neighborhood of each node.
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The average degree of a node `i` is
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k_{nn,i} = \frac{1}{|N(i)|} \sum_{j \in N(i)} k_j
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where `N(i)` are the neighbors of node `i` and `k_j` is
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the degree of node `j` which belongs to `N(i)`. For weighted
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graphs, an analogous measure can be defined [1]_,
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k_{nn,i}^{w} = \frac{1}{s_i} \sum_{j \in N(i)} w_{ij} k_j
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where `s_i` is the weighted degree of node `i`, `w_{ij}`
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is the weight of the edge that links `i` and `j` and
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`N(i)` are the neighbors of node `i`.
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source : string ("in"|"out")
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Use "in"- or "out"-degree for source node.
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target : string ("in"|"out")
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Use "in"- or "out"-degree for target node.
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nodes : list or iterable, optional
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Compute neighbor degree for specified nodes. The default is
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all nodes in the graph.
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weight : string or None, optional (default=None)
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The edge attribute that holds the numerical value used as a weight.
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If None, then each edge has weight 1.
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A dictionary keyed by node with average neighbors degree value.
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>>> G=nx.path_graph(4)
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>>> G.edge[0][1]['weight'] = 5
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>>> G.edge[2][3]['weight'] = 3
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>>> nx.average_neighbor_degree(G)
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{0: 2.0, 1: 1.5, 2: 1.5, 3: 2.0}
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>>> nx.average_neighbor_degree(G, weight='weight')
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{0: 2.0, 1: 1.1666666666666667, 2: 1.25, 3: 2.0}
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>>> G.add_path([0,1,2,3])
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>>> nx.average_neighbor_degree(G, source='in', target='in')
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{0: 1.0, 1: 1.0, 2: 1.0, 3: 0.0}
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>>> nx.average_neighbor_degree(G, source='out', target='out')
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{0: 1.0, 1: 1.0, 2: 0.0, 3: 0.0}
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For directed graphs you can also specify in-degree or out-degree
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by passing keyword arguments.
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average_degree_connectivity
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.. [1] A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani,
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"The architecture of complex weighted networks".
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PNAS 101 (11): 3747–3752 (2004).
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source_degree = G.degree
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target_degree = G.degree
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direction = {'out':G.out_degree,
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source_degree = direction[source]
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target_degree = direction[target]
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return _average_nbr_deg(G, source_degree, target_degree,
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nodes=nodes, weight=weight)
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# def average_neighbor_in_degree(G, nodes=None, weight=None):
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# if not G.is_directed():
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# raise nx.NetworkXError("Not defined for undirected graphs.")
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# return _average_nbr_deg(G, G.in_degree, G.in_degree, nodes, weight)
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# average_neighbor_in_degree.__doc__=average_neighbor_degree.__doc__
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# def average_neighbor_out_degree(G, nodes=None, weight=None):
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# if not G.is_directed():
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# raise nx.NetworkXError("Not defined for undirected graphs.")
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# return _average_nbr_deg(G, G.out_degree, G.out_degree, nodes, weight)
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# average_neighbor_out_degree.__doc__=average_neighbor_degree.__doc__
added
removed
networkx/algorithms/assortativity/neighbor_degree.py
