lib/python2.7/site-packages/setoolsgui/networkx/algorithms/link_analysis/pagerank_alg.py

"""PageRank analysis of graph structure. """
#    Copyright (C) 2004-2011 by
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.
#    NetworkX:http://networkx.lanl.gov/
import networkx as nx
from networkx.exception import NetworkXError
__author__ = """Aric Hagberg (hagberg@lanl.gov)"""
__all__ = ['pagerank','pagerank_numpy','pagerank_scipy','google_matrix']

def pagerank(G,alpha=0.85,personalization=None,
             max_iter=100,tol=1.0e-8,nstart=None,weight='weight'):
    """Return the PageRank of the nodes in the graph.

    PageRank computes a ranking of the nodes in the graph G based on
    the structure of the incoming links. It was originally designed as
    an algorithm to rank web pages.

    Parameters
    -----------
    G : graph
      A NetworkX graph

    alpha : float, optional
      Damping parameter for PageRank, default=0.85

    personalization: dict, optional
       The "personalization vector" consisting of a dictionary with a
       key for every graph node and nonzero personalization value for each node.

    max_iter : integer, optional
      Maximum number of iterations in power method eigenvalue solver.

    tol : float, optional
      Error tolerance used to check convergence in power method solver.

    nstart : dictionary, optional
      Starting value of PageRank iteration for each node.

    weight : key, optional
      Edge data key to use as weight.  If None weights are set to 1.

    Returns
    -------
    pagerank : dictionary
       Dictionary of nodes with PageRank as value

    Examples
    --------
    >>> G=nx.DiGraph(nx.path_graph(4))
    >>> pr=nx.pagerank(G,alpha=0.9)

    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.

    The PageRank algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs by converting each oriented edge in the
    directed graph to two edges.

    See Also
    --------
    pagerank_numpy, pagerank_scipy, google_matrix

    References
    ----------
    .. [1] A. Langville and C. Meyer,
       "A survey of eigenvector methods of web information retrieval."
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry,
       The PageRank citation ranking: Bringing order to the Web. 1999
       http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf
    """
    if type(G) == nx.MultiGraph or type(G) == nx.MultiDiGraph:
        raise Exception("pagerank() not defined for graphs with multiedges.")

    if len(G) == 0:
        return {}

    if not G.is_directed():
        D=G.to_directed()
    else:
        D=G

    # create a copy in (right) stochastic form
    W=nx.stochastic_graph(D, weight=weight)
    scale=1.0/W.number_of_nodes()

    # choose fixed starting vector if not given
    if nstart is None:
        x=dict.fromkeys(W,scale)
    else:
        x=nstart
        # normalize starting vector to 1
        s=1.0/sum(x.values())
        for k in x: x[k]*=s

    # assign uniform personalization/teleportation vector if not given
    if personalization is None:
        p=dict.fromkeys(W,scale)
    else:
        p=personalization
        # normalize starting vector to 1
        s=1.0/sum(p.values())
        for k in p:
            p[k]*=s
        if set(p)!=set(G):
            raise NetworkXError('Personalization vector '
                                'must have a value for every node')


    # "dangling" nodes, no links out from them
    out_degree=W.out_degree()
    dangle=[n for n in W if out_degree[n]==0.0]
    i=0
    while True: # power iteration: make up to max_iter iterations
        xlast=x
        x=dict.fromkeys(xlast.keys(),0)
        danglesum=alpha*scale*sum(xlast[n] for n in dangle)
        for n in x:
            # this matrix multiply looks odd because it is
            # doing a left multiply x^T=xlast^T*W
            for nbr in W[n]:
                x[nbr]+=alpha*xlast[n]*W[n][nbr][weight]
            x[n]+=danglesum+(1.0-alpha)*p[n]
        # normalize vector
        s=1.0/sum(x.values())
        for n in x:
            x[n]*=s
        # check convergence, l1 norm
        err=sum([abs(x[n]-xlast[n]) for n in x])
        if err < tol:
            break
        if i>max_iter:
            raise NetworkXError('pagerank: power iteration failed to converge '
                                'in %d iterations.'%(i-1))
        i+=1
    return x


def google_matrix(G, alpha=0.85, personalization=None,
                  nodelist=None, weight='weight'):
    """Return the Google matrix of the graph.

    Parameters
    -----------
    G : graph
      A NetworkX graph

    alpha : float
      The damping factor

    personalization: dict, optional
       The "personalization vector" consisting of a dictionary with a
       key for every graph node and nonzero personalization value for each node.

    nodelist : list, optional
      The rows and columns are ordered according to the nodes in nodelist.
      If nodelist is None, then the ordering is produced by G.nodes().

    weight : key, optional
      Edge data key to use as weight.  If None weights are set to 1.

    Returns
    -------
    A : NumPy matrix
       Google matrix of the graph

    See Also
    --------
    pagerank, pagerank_numpy, pagerank_scipy
    """
    try:
        import numpy as np
    except ImportError:
        raise ImportError(\
            "google_matrix() requires NumPy: http://scipy.org/")
    # choose ordering in matrix
    if personalization is None: # use G.nodes() ordering
        nodelist=G.nodes()
    else:  # use personalization "vector" ordering
        nodelist=personalization.keys()
        if set(nodelist)!=set(G):
            raise NetworkXError('Personalization vector dictionary'
                                'must have a value for every node')
    M=nx.to_numpy_matrix(G,nodelist=nodelist,weight=weight)
    (n,m)=M.shape # should be square
    if n == 0:
        return M
    # add constant to dangling nodes' row
    dangling=np.where(M.sum(axis=1)==0)
    for d in dangling[0]:
        M[d]=1.0/n
    # normalize
    M=M/M.sum(axis=1)
    # add "teleportation"/personalization
    e=np.ones((n))
    if personalization is not None:
        v=np.array(list(personalization.values()),dtype=float)
    else:
        v=e
    v=v/v.sum()
    P=alpha*M+(1-alpha)*np.outer(e,v)
    return P


def pagerank_numpy(G, alpha=0.85, personalization=None, weight='weight'):
    """Return the PageRank of the nodes in the graph.

    PageRank computes a ranking of the nodes in the graph G based on
    the structure of the incoming links. It was originally designed as
    an algorithm to rank web pages.

    Parameters
    -----------
    G : graph
      A NetworkX graph

    alpha : float, optional
      Damping parameter for PageRank, default=0.85

    personalization: dict, optional
       The "personalization vector" consisting of a dictionary with a
       key for every graph node and nonzero personalization value for each node.

    weight : key, optional
      Edge data key to use as weight.  If None weights are set to 1.

    Returns
    -------
    pagerank : dictionary
       Dictionary of nodes with PageRank as value

    Examples
    --------
    >>> G=nx.DiGraph(nx.path_graph(4))
    >>> pr=nx.pagerank_numpy(G,alpha=0.9)

    Notes
    -----
    The eigenvector calculation uses NumPy's interface to the LAPACK
    eigenvalue solvers.  This will be the fastest and most accurate
    for small graphs.

    This implementation works with Multi(Di)Graphs.

    See Also
    --------
    pagerank, pagerank_scipy, google_matrix

    References
    ----------
    .. [1] A. Langville and C. Meyer,
       "A survey of eigenvector methods of web information retrieval."
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry,
       The PageRank citation ranking: Bringing order to the Web. 1999
       http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf
    """
    try:
        import numpy as np
    except ImportError:
        raise ImportError("pagerank_numpy() requires NumPy: http://scipy.org/")
    if len(G) == 0:
        return {}
    # choose ordering in matrix
    if personalization is None: # use G.nodes() ordering
        nodelist=G.nodes()
    else:  # use personalization "vector" ordering
        nodelist=personalization.keys()
    M=google_matrix(G, alpha, personalization=personalization,
                    nodelist=nodelist, weight=weight)
    # use numpy LAPACK solver
    eigenvalues,eigenvectors=np.linalg.eig(M.T)
    ind=eigenvalues.argsort()
    # eigenvector of largest eigenvalue at ind[-1], normalized
    largest=np.array(eigenvectors[:,ind[-1]]).flatten().real
    norm=float(largest.sum())
    centrality=dict(zip(nodelist,map(float,largest/norm)))
    return centrality


def pagerank_scipy(G, alpha=0.85, personalization=None,
                   max_iter=100, tol=1.0e-6, weight='weight'):
    """Return the PageRank of the nodes in the graph.

    PageRank computes a ranking of the nodes in the graph G based on
    the structure of the incoming links. It was originally designed as
    an algorithm to rank web pages.

    Parameters
    -----------
    G : graph
      A NetworkX graph

    alpha : float, optional
      Damping parameter for PageRank, default=0.85

    personalization: dict, optional
       The "personalization vector" consisting of a dictionary with a
       key for every graph node and nonzero personalization value for each node.

    max_iter : integer, optional
      Maximum number of iterations in power method eigenvalue solver.

    tol : float, optional
      Error tolerance used to check convergence in power method solver.

    weight : key, optional
      Edge data key to use as weight.  If None weights are set to 1.

    Returns
    -------
    pagerank : dictionary
       Dictionary of nodes with PageRank as value

    Examples
    --------
    >>> G=nx.DiGraph(nx.path_graph(4))
    >>> pr=nx.pagerank_scipy(G,alpha=0.9)

    Notes
    -----
    The eigenvector calculation uses power iteration with a SciPy
    sparse matrix representation.

    See Also
    --------
    pagerank, pagerank_numpy, google_matrix

    References
    ----------
    .. [1] A. Langville and C. Meyer,
       "A survey of eigenvector methods of web information retrieval."
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Page, Lawrence; Brin, Sergey; Motwani, Rajeev and Winograd, Terry,
       The PageRank citation ranking: Bringing order to the Web. 1999
       http://dbpubs.stanford.edu:8090/pub/showDoc.Fulltext?lang=en&doc=1999-66&format=pdf
    """
    try:
        import scipy.sparse
    except ImportError:
        raise ImportError("pagerank_scipy() requires SciPy: http://scipy.org/")
    if len(G) == 0:
        return {}
    # choose ordering in matrix
    if personalization is None: # use G.nodes() ordering
        nodelist=G.nodes()
    else:  # use personalization "vector" ordering
        nodelist=personalization.keys()
    M=nx.to_scipy_sparse_matrix(G,nodelist=nodelist,weight=weight,dtype='f')
    (n,m)=M.shape # should be square
    S=scipy.array(M.sum(axis=1)).flatten()
#    for i, j, v in zip( *scipy.sparse.find(M) ):
#        M[i,j] = v / S[i]
    S[S>0] = 1.0 / S[S>0]
    Q = scipy.sparse.spdiags(S.T, 0, *M.shape, format='csr')
    M = Q * M
    x=scipy.ones((n))/n  # initial guess
    dangle=scipy.array(scipy.where(M.sum(axis=1)==0,1.0/n,0)).flatten()
    # add "teleportation"/personalization
    if personalization is not None:
        v=scipy.array(list(personalization.values()),dtype=float)
        v=v/v.sum()
    else:
        v=x
    i=0
    while i <= max_iter:
        # power iteration: make up to max_iter iterations
        xlast=x
        x=alpha*(x*M+scipy.dot(dangle,xlast))+(1-alpha)*v
        x=x/x.sum()
        # check convergence, l1 norm
        err=scipy.absolute(x-xlast).sum()
        if err < n*tol:
            return dict(zip(nodelist,map(float,x)))
        i+=1
    raise NetworkXError('pagerank_scipy: power iteration failed to converge'
                        'in %d iterations.'%(i+1))


# fixture for nose tests
def setup_module(module):
    from nose import SkipTest
    try:
        import numpy
    except:
        raise SkipTest("NumPy not available")
    try:
        import scipy
    except:
        raise SkipTest("SciPy not available")