Spaces:
Running
Running
| """ | |
| Spectral bipartivity measure. | |
| """ | |
| import networkx as nx | |
| __all__ = ["spectral_bipartivity"] | |
| 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 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[i, i] / expA[i, i] | |
| return sb | |