69 lines
1.8 KiB
Python
69 lines
1.8 KiB
Python
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"""
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Spectral bipartivity measure.
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"""
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import networkx as nx
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__all__ = ["spectral_bipartivity"]
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def spectral_bipartivity(G, nodes=None, weight="weight"):
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"""Returns the spectral bipartivity.
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Parameters
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----------
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G : NetworkX graph
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nodes : list or container optional(default is all nodes)
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Nodes to return value of spectral bipartivity contribution.
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weight : string or None optional (default = 'weight')
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Edge data key to use for edge weights. If None, weights set to 1.
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Returns
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-------
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sb : float or dict
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A single number if the keyword nodes is not specified, or
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a dictionary keyed by node with the spectral bipartivity contribution
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of that node as the value.
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Examples
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--------
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>>> from networkx.algorithms import bipartite
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>>> G = nx.path_graph(4)
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>>> bipartite.spectral_bipartivity(G)
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1.0
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Notes
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-----
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This implementation uses Numpy (dense) matrices which are not efficient
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for storing large sparse graphs.
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See Also
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--------
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color
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References
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----------
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.. [1] E. Estrada and J. A. Rodríguez-Velázquez, "Spectral measures of
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bipartivity in complex networks", PhysRev E 72, 046105 (2005)
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"""
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import scipy as sp
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import scipy.linalg # call as sp.linalg
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nodelist = list(G) # ordering of nodes in matrix
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A = nx.to_numpy_array(G, nodelist, weight=weight)
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expA = sp.linalg.expm(A)
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expmA = sp.linalg.expm(-A)
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coshA = 0.5 * (expA + expmA)
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if nodes is None:
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# return single number for entire graph
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return coshA.diagonal().sum() / expA.diagonal().sum()
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else:
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# contribution for individual nodes
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index = dict(zip(nodelist, range(len(nodelist))))
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sb = {}
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for n in nodes:
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i = index[n]
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sb[n] = coshA[i, i] / expA[i, i]
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return sb
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