Centralidad del vector propio (medida de centralidad)

def eigenvector_centrality(G, max_iter=100, tol=1.0e-6, nstart=None,
                           weight='weight'):
    """Compute the eigenvector centrality for the graph G.
  
    Eigenvector centrality computes the centrality for a node based on the
    centrality of its neighbors. The eigenvector centrality for node `i` is
  
    .. math::
  
        \mathbf{Ax} = \lambda \mathbf{x}
  
    where `A` is the adjacency matrix of the graph G with eigenvalue `\lambda`.
    By virtue of the Perron–Frobenius theorem, there is a unique and positive
    solution if `\lambda` is the largest eigenvalue associated with the
    eigenvector of the adjacency matrix `A` ([2]_).
  
    Parameters
    ----------
    G : graph
      A networkx graph
  
    max_iter : integer, optional
      Maximum number of iterations in power method.
  
    tol : float, optional
      Error tolerance used to check convergence in power method iteration.
  
    nstart : dictionary, optional
      Starting value of eigenvector iteration for each node.
  
    weight : None or string, optional
      If None, all edge weights are considered equal.
      Otherwise holds the name of the edge attribute used as weight.
  
    Returns
    -------
    nodes : dictionary
       Dictionary of nodes with eigenvector centrality as the value.
  
        
    Notes
    ------
    The eigenvector calculation is done by the power iteration method and has
    no guarantee of convergence. The iteration will stop after ``max_iter``
    iterations or an error tolerance of ``number_of_nodes(G)*tol`` has been
    reached.
  
    For directed graphs this is "left" eigenvector centrality which corresponds
    to the in-edges in the graph. For out-edges eigenvector centrality
    first reverse the graph with ``G.reverse()``.
  
     
    """
    from math import sqrt
    if type(G) == nx.MultiGraph or type(G) == nx.MultiDiGraph:
        raise nx.NetworkXException("Not defined for multigraphs.")
  
    if len(G) == 0:
        raise nx.NetworkXException("Empty graph.")
  
    if nstart is None:
  
        # choose starting vector with entries of 1/len(G)
        x = dict([(n,1.0/len(G)) for n in G])
    else:
        x = nstart
  
    # normalize starting vector
    s = 1.0/sum(x.values())
    for k in x:
        x[k] *= s
    nnodes = G.number_of_nodes()
  
    # make up to max_iter iterations
    for i in range(max_iter):
        xlast = x
        x = dict.fromkeys(xlast, 0)
  
        # do the multiplication y^T = x^T A
        for n in x:
            for nbr in G[n]:
                x[nbr] += xlast[n] * G[n][nbr].get(weight, 1)
  
        # normalize vector
        try:
            s = 1.0/sqrt(sum(v**2 for v in x.values()))
  
        # this should never be zero?
        except ZeroDivisionError:
            s = 1.0
        for n in x:
            x[n] *= s
  
        # check convergence
        err = sum([abs(x[n]-xlast[n]) for n in x])
        if err < nnodes*tol:
            return x
  
    raise nx.NetworkXError("""eigenvector_centrality():
power iteration failed to converge in %d iterations."%(i+1))""")

>>> import networkx as nx
>>> G = nx.path_graph(4)
>>> centrality = nx.eigenvector_centrality(G)
>>> print(['%s %0.2f'%(node,centrality[node]) for node in centrality])

['0 0.37', '1 0.60', '2 0.60', '3 0.37']