Source code for networkx.algorithms.bipartite.spectral

Spectral bipartivity measure.
import networkx as nx

__all__ = ["spectral_bipartivity"]

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