def pagerank_numpy(G, alpha=0.85, personalization=None, weight='weight', dangling=None):
 import numpy as np
 if (len(G) == 0):
  return {}
 M = google_matrix(G, alpha, personalization=personalization, weight=weight, dangling=dangling)
 (eigenvalues, eigenvectors) = np.linalg.eig(M.T)
 ind = np.argmax(eigenvalues)
 largest = np.array(eigenvectors[:, ind]).flatten().real
 norm = float(largest.sum())
 return dict(zip(G, map(float, (largest / norm))))

def pagerank_numpy ( G , alpha = 0.85 , personalization = None , weight = 'weight' , dangling = None ) : import numpy as np if ( len ( G ) == 0 ) : return { } M = google_matrix ( G , alpha , personalization = personalization , weight = weight , dangling = dangling ) ( eigenvalues , eigenvectors ) = np . linalg . eig ( M . T ) ind = np . argmax ( eigenvalues ) largest = np . array ( eigenvectors [ : , ind ] ) . flatten ( ) . real norm = float ( largest . sum ( ) ) return dict ( zip ( G , map ( float , ( largest / norm ) ) ) )
return the pagerank of the nodes in the graph .