Python networkx.is_aperiodic函数代码示例

def test_is_aperiodic_disconnected():
    # disconnected graph
    G = nx.DiGraph()
    nx.add_cycle(G, [1, 2, 3, 4])
    nx.add_cycle(G, [5, 6, 7, 8])
    assert_false(nx.is_aperiodic(G))
    G.add_edge(1, 3)
    G.add_edge(5, 7)
    assert_true(nx.is_aperiodic(G))

def output_aperiodicity_info (graph, path):
    """Output aperiodicity information about the graph.
       graph : (networkx.Graph)
       path: (String) contains the path to the output file
    """
    with open(path, 'w') as out:
        out.write('***Aperiodicity***\n')
        out.write('Is aperiodic: %s' % nx.is_aperiodic(graph))

def is_aperiodic(G):
    """Return True if G is aperiodic.

    A directed graph is aperiodic if there is no integer k > 1 that
    divides the length of every cycle in the graph.

    Parameters
    ----------
    G : NetworkX DiGraph
        Graph

    Returns
    -------
    aperiodic : boolean
        True if the graph is aperiodic False otherwise

    Raises
    ------
    NetworkXError
        If G is not directed

    Notes
    -----
    This uses the method outlined in [1]_, which runs in O(m) time
    given m edges in G. Note that a graph is not aperiodic if it is
    acyclic as every integer trivial divides length 0 cycles.

    References
    ----------
    .. [1] Jarvis, J. P.; Shier, D. R. (1996),
       Graph-theoretic analysis of finite Markov chains,
       in Shier, D. R.; Wallenius, K. T., Applied Mathematical Modeling:
       A Multidisciplinary Approach, CRC Press.
    """
    if not G.is_directed():
        raise nx.NetworkXError(
            "is_aperiodic not defined for undirected graphs")

    s = arbitrary_element(G)
    levels = {s: 0}
    this_level = [s]
    g = 0
    l = 1
    while this_level:
        next_level = []
        for u in this_level:
            for v in G[u]:
                if v in levels:  # Non-Tree Edge
                    g = gcd(g, levels[u] - levels[v] + 1)
                else:  # Tree Edge
                    next_level.append(v)
                    levels[v] = l
        this_level = next_level
        l += 1
    if len(levels) == len(G):  # All nodes in tree
        return g == 1
    else:
        return g == 1 and nx.is_aperiodic(G.subgraph(set(G) - set(levels)))

def test_networkx_methods():
    reducible_G = nx.DiGraph(np.matrix([[1,0],[0,1]]))
    print 'reducible- is strongly connected? ' + str(nx.is_strongly_connected(reducible_G)) #False
    print 'reducible- strongly connected components: ' + str(nx.strongly_connected_components(reducible_G)) #[[0], [1]]
    print 'reducible- is aperiodic? ' + str(nx.is_aperiodic(reducible_G)) #True
    
    irreducible_periodic_G = nx.DiGraph(np.matrix([[0,1],[1,0]]))
    print '\nirreducible_periodic- is strongly connected? ' + str(nx.is_strongly_connected(irreducible_periodic_G)) #True
    print 'irreducible_periodic- strongly connected components: ' + str(nx.strongly_connected_components(irreducible_periodic_G)) #[[0, 1]]
    print 'irreducible_periodic- is aperiodic? ' + str(nx.is_aperiodic(irreducible_periodic_G)) #False (2)
    
    ergodic_G = nx.DiGraph(np.matrix([[0,1,1,0],[1,0,0,1],[0,1,0,0],[0,1,0,0]]))
    modified_G = nx.DiGraph(salsa.get_matrix(ergodic_G, mat_type='hub', sparse=False))
    print 'modified- is strongly connected? ' + str(nx.is_strongly_connected(modified_G)) #False
    print 'modified- strongly connected components: ' + str(nx.strongly_connected_components(modified_G)) #[[0, 2, 3], [1]]
    print 'modified- is aperiodic? ' + str(nx.is_aperiodic(modified_G)) #True

    return

def test_eig_error():
    #graph_file = '/home/michal/SALSA_files/tmp/real_run/graph_11'
    #G = gm.read_graph_from_file(graph_file)
    graph_list = [(354, 354, {'weight': 0.5}),\
                  (354, 13291, {'weight': 0.25}),\
                  (354, 11354, {'weight': 0.25}),\
                  (15204, 15204, {'weight': 0.5}),\
                  (15204, 14639, {'weight': 0.5}),\
                  (11210, 6898, {'weight': 0.25}),\
                  (11210, 11210, {'weight': 0.5}),\
                  (11210, 11354, {'weight': 0.25}),\
                  (13291, 354, {'weight': 0.5}),\
                  (13291, 13291, {'weight': 0.5}),\
                  (14639, 13236, {'weight': 0.16666666666666666}),\
                  (14639, 6898, {'weight': 0.16666666666666666}),\
                  (14639, 15204, {'weight': 0.25}),\
                  (14639, 14639, {'weight': 0.41666666666666663}),\
                  (6898, 6898, {'weight': 0.6111111111111112}),\
                  (6898, 13236, {'weight': 0.1111111111111111}),\
                  (6898, 11210, {'weight': 0.16666666666666666}),\
                  (6898, 14639, {'weight': 0.1111111111111111}),\
                  (13236, 6898, {'weight': 0.3333333333333333}),\
                  (13236, 13236, {'weight': 0.3333333333333333}),\
                  (13236, 14639, {'weight': 0.3333333333333333}),\
                  (11354, 11210, {'weight': 0.25}),\
                  (11354, 354, {'weight': 0.25}),\
                  (11354, 11354, {'weight': 0.5})]
    #(11354, 11354, {'weight': 0.5})]

    G = nx.DiGraph(graph_list)
    #print G.edges(data=True)
    print '--- eig_calc: is sub graph stochastic? ' + str(gm.check_if_stochastic_matrix(nx.to_numpy_matrix(G)))#; sys.stdout.flush()
    print '--- eig_calc: is sub graph strongly connected? ' + str(nx.is_strongly_connected(G))#; sys.stdout.flush()
    print '--- eig_calc: is sub graph aperiodic? ' + str(nx.is_aperiodic(G));# sys.stdout.flush()
    #np_mat = nx.to_numpy_matrix(G)
    #print 'det= '+ str(np.linalg.det(np_mat))
    print salsa.eig_calc(G)
    '''try:
        print salsa.eig_calc(G)
    except RuntimeError: 
        max_weight = max(e[2]['weight'] for e in G.edges_iter(data=True))
        noise = 1e-13
        for e in G.edges_iter(data=True):
            if e[2]['weight'] == max_weight:
                e[2]['weight'] += noise
        if not gm.check_if_stochastic_matrix(nx.to_numpy_matrix(G)):
            nx.stochastic_graph(G, copy=False)
        print salsa.eig_calc(G)'''
    
    

    
    return

def test_is_aperiodic_bipartite():
    # Bipartite graph
    G = nx.DiGraph(nx.davis_southern_women_graph())
    assert_false(nx.is_aperiodic(G))

def test_is_aperiodic_selfloop():
    G = nx.DiGraph()
    nx.add_cycle(G, [1, 2, 3, 4])
    G.add_edge(1, 1)
    assert_true(nx.is_aperiodic(G))

def test_is_aperiodic_cycle3():
    G = nx.DiGraph()
    nx.add_cycle(G, [1, 2, 3, 4])
    nx.add_cycle(G, [3, 4, 5, 6])
    assert_false(nx.is_aperiodic(G))

def test_is_aperiodic_cycle2():
    G = nx.DiGraph()
    nx.add_cycle(G, [1, 2, 3, 4])
    nx.add_cycle(G, [3, 4, 5, 6, 7])
    assert_true(nx.is_aperiodic(G))

def _transition_matrix(G, nodelist=None, weight='weight',
                       walk_type=None, alpha=0.95):
    """Returns the transition matrix of G.

    This is a row stochastic giving the transition probabilities while
    performing a random walk on the graph. Depending on the value of walk_type,
    P can be the transition matrix induced by a random walk, a lazy random walk,
    or a random walk with teleportation (PageRank).

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

    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 : string or None, optional (default='weight')
       The edge data key used to compute each value in the matrix.
       If None, then each edge has weight 1.

    walk_type : string or None, optional (default=None)
       If None, `P` is selected depending on the properties of the
       graph. Otherwise is one of 'random', 'lazy', or 'pagerank'

    alpha : real
       (1 - alpha) is the teleportation probability used with pagerank

    Returns
    -------
    P : NumPy array
      transition matrix of G.

    Raises
    ------
    NetworkXError
        If walk_type not specified or alpha not in valid range
    """

    import scipy as sp
    from scipy.sparse import identity, spdiags
    if walk_type is None:
        if nx.is_strongly_connected(G):
            if nx.is_aperiodic(G):
                walk_type = "random"
            else:
                walk_type = "lazy"
        else:
            walk_type = "pagerank"

    M = nx.to_scipy_sparse_matrix(G, nodelist=nodelist, weight=weight,
                                  dtype=float)
    n, m = M.shape
    if walk_type in ["random", "lazy"]:
        DI = spdiags(1.0 / sp.array(M.sum(axis=1).flat), [0], n, n)
        if walk_type == "random":
            P = DI * M
        else:
            I = identity(n)
            P = (I + DI * M) / 2.0

    elif walk_type == "pagerank":
        if not (0 < alpha < 1):
            raise nx.NetworkXError('alpha must be between 0 and 1')
        # this is using a dense representation
        M = M.todense()
        # add constant to dangling nodes' row
        dangling = sp.where(M.sum(axis=1) == 0)
        for d in dangling[0]:
            M[d] = 1.0 / n
        # normalize
        M = M / M.sum(axis=1)
        P = alpha * M + (1 - alpha) / n
    else:
        raise nx.NetworkXError("walk_type must be random, lazy, or pagerank")

    return P

def directed_laplacian_matrix(G, nodelist=None, weight='weight',
                              walk_type=None, alpha=0.95):
    r"""Return the directed Laplacian matrix of G.

    The graph directed Laplacian is the matrix

    .. math::

        L = I - (\Phi^{1/2} P \Phi^{-1/2} + \Phi^{-1/2} P^T \Phi^{1/2} ) / 2

    where `I` is the identity matrix, `P` is the transition matrix of the
    graph, and `\Phi` a matrix with the Perron vector of `P` in the diagonal and
    zeros elsewhere.

    Depending on the value of walk_type, `P` can be the transition matrix
    induced by a random walk, a lazy random walk, or a random walk with
    teleportation (PageRank).

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

    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 : string or None, optional (default='weight')
       The edge data key used to compute each value in the matrix.
       If None, then each edge has weight 1.

    walk_type : string or None, optional (default=None)
       If None, `P` is selected depending on the properties of the
       graph. Otherwise is one of 'random', 'lazy', or 'pagerank'

    alpha : real
       (1 - alpha) is the teleportation probability used with pagerank

    Returns
    -------
    L : NumPy array
      Normalized Laplacian of G.

    Raises
    ------
    NetworkXError
        If NumPy cannot be imported

    NetworkXNotImplemnted
        If G is not a DiGraph

    Notes
    -----
    Only implemented for DiGraphs

    See Also
    --------
    laplacian_matrix

    References
    ----------
    .. [1] Fan Chung (2005).
       Laplacians and the Cheeger inequality for directed graphs.
       Annals of Combinatorics, 9(1), 2005
    """
    import scipy as sp
    from scipy.sparse import identity, spdiags, linalg
    if walk_type is None:
        if nx.is_strongly_connected(G):
            if nx.is_aperiodic(G):
                walk_type = "random"
            else:
                walk_type = "lazy"
        else:
            walk_type = "pagerank"

    M = nx.to_scipy_sparse_matrix(G, nodelist=nodelist, weight=weight,
                                  dtype=float)
    n, m = M.shape
    if walk_type in ["random", "lazy"]:
        DI = spdiags(1.0/sp.array(M.sum(axis=1).flat), [0], n, n)
        if walk_type == "random":
            P =  DI * M
        else:
            I = identity(n)
            P = (I + DI * M) / 2.0

    elif walk_type == "pagerank":
        if not (0 < alpha < 1):
            raise nx.NetworkXError('alpha must be between 0 and 1')
        # this is using a dense representation
        M = M.todense()
        # add constant to dangling nodes' row
        dangling = sp.where(M.sum(axis=1) == 0)
        for d in dangling[0]:
            M[d] = 1.0 / n
        # normalize
        M = M / M.sum(axis=1)
        P = alpha * M + (1 - alpha) / n
    else:
#.........这里部分代码省略.........

def salsa_numpy(G,normalized=True):
    """Return HITS hubs and authorities values for nodes.

    The HITS algorithm computes two numbers for a node.
    Authorities estimates the node value based on the incoming links.
    Hubs estimates the node value based on outgoing links.

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

    normalized : bool (default=True)
       Normalize results by the sum of all of the values.

    Returns
    -------
    (hubs,authorities) : two-tuple of dictionaries
       Two dictionaries keyed by node containing the hub and authority
       values.

    Examples
    --------
    >>> G=nx.path_graph(4)
    >>> h,a=nx.hits(G)

    Notes
    -----
    The eigenvector calculation uses NumPy's interface to LAPACK.

    The HITS algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs.

    References
    ----------
    .. [1] A. Langville and C. Meyer,
       "A survey of eigenvector methods of web information retrieval."
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Jon Kleinberg,
       Authoritative sources in a hyperlinked environment
       Journal of the ACM 46 (5): 604-32, 1999.
       doi:10.1145/324133.324140.
       http://www.cs.cornell.edu/home/kleinber/auth.pdf.
    """
    print '\n\t~~~~~~ salsa_numpy (eigenvector calc) ~~~~~~\n'
    try:
        import numpy as np
        import scipy as sp
    except ImportError:
        raise ImportError(\
            "hits_numpy() requires NumPy: http://scipy.org/")
    if len(G) == 0:
        return {},{}
    print '--- salsa_numpy: start time- ' + str(datetime.now())
    startTime = datetime.now()      
    #np.set_printoptions(precision=3)    # For printing numpy objects- prints 3 decimal after the point.
    H_sparse = get_matrix(G,mat_type='hub',sparse=True)
    print '--- salsa_numpy: get_matrix (hub) took: '+str(datetime.now()-startTime); tmpTime = datetime.now()
    eps = gm.epsilon
    # DEBUG:
    new_G_h = nx.DiGraph(H_sparse)
    print 'is new graph strongly connected? ' + str(nx.is_strongly_connected(new_G_h))
    print 'is new graph aperiodic? ' + str(nx.is_aperiodic(new_G_h))
    #H = gm.convert_all_matrix_zeros_to_val(H_sparse, val=eps, stochastic_out=True)
    #print '--- salsa_numpy: convert_all_matrix_zeros_to_eps took: '+str(datetime.now()-tmpTime); tmpTime = datetime.now()
    H = H_sparse.todense() 
    #e,ev=np.linalg.eig(H)
    e,ev=sp.linalg.eig(H,left=True,right=False)
    #e,ev=np.linalg.eig(H.T) #we send H.T for calculating the LEFT eigenvector!
    print '--- salsa_numpy: calculating hub eigs took: ' + str(datetime.now()-tmpTime)
    
    #e,ev=sps.linalg.eigs(H,left=True,right=False)
    m=e.argsort()[-1] # index of maximum eigenvalue
    '''#DEBUG: 
    print('\nH:\n' + str(H.round(3)))
    print'\ne rounded (3)\n' + str(e.round(3)) + '\nev rounded (3)\n' + str(ev.round(3))
    print 'm- index of maximum eigenvalue= ' + str(m) + ',  max eigenvalue= ' + str(e[m]) + \
        '\nev rounded (3)\n' + str(np.array(ev[:,m]).flatten().round(3))'''
    h=np.array(ev[:,m]).flatten()
    # DEBUG:
    print h
    
    tmpTime = datetime.now()
    
    A_sparse = get_matrix(G,mat_type='authority',sparse=True)
    print '--- salsa_numpy: get_matrix (authority) took: '+str(datetime.now()-tmpTime); tmpTime = datetime.now()
    new_G_a = nx.DiGraph(A_sparse)
    print 'is new graph strongly connected? ' + str(nx.is_strongly_connected(new_G_a))
    print 'is new graph aperiodic? ' + str(nx.is_aperiodic(new_G_a))
    #A = gm.convert_all_matrix_zeros_to_val(A_sparse, val=eps, stochastic_out=True)
    #print '--- salsa_numpy: convert_all_matrix_zeros_to_eps took: '+str(datetime.now()-tmpTime); tmpTime = datetime.now()
    A = A_sparse.todense() 
    e,ev=sp.linalg.eig(A,left=True,right=False)
    #e,ev=sps.linalg.eigs(A,left=True,right=False)
    #e,ev=np.linalg.eig(A.T) #we send A.T for calculating the LEFT eigenvector!
    print '--- salsa_numpy: calculating hub eigs took: ' + str(datetime.now()-tmpTime)
    m=e.argsort()[-1] # index of maximum eigenvalue  
    a=np.array(ev[:,m]).flatten()
    '''#DEBUG: 
#.........这里部分代码省略.........

def test_is_aperiodic_disconnected2():
    G = nx.DiGraph()
    nx.add_cycle(G, [0, 1, 2])
    G.add_edge(3, 3)
    assert_false(nx.is_aperiodic(G))

# components
nx.is_strongly_connected(G)
nx.number_strongly_connected_components(G)
scc = nx.strongly_connected_components(G)
nx.strongly_connected_components_recursive(G)
nx.condensation(G, scc)

# attracting components
nx.is_attracting_component(G)
nx.number_attracting_components(G)
nx.attracting_components(G)

# directed acyclic graphs
nx.is_directed_acyclic_graph(G)
nx.is_aperiodic(G)

# distance measure  (all for connected graph)
nx.center(Gcc)
nx.diameter(Gcc)
nx.eccentricity(Gcc) 
nx.periphery(Gcc)
nx.radius(Gcc)

# flows (seg fault currently)
#nx.max_flow(Gcc, 1, 2)
#nx.min_cut(G, 1, 2)

# isolates
nx.is_isolate(G, 1)     # False
nx.is_isolate(G, 5)     # True

def salsa_scipy_old(G,max_iter=100,tol=1.0e-6,nstart_dict=None,normalized=True, debug=False):
    """Return HITS hubs and authorities values for nodes.

    The HITS algorithm computes two numbers for a node.
    Authorities estimates the node value based on the incoming links.
    Hubs estimates the node value based on outgoing links.

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

    max_iter : interger, 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 each node for power method iteration.

    normalized : bool (default=True)
       Normalize results by the sum of all of the values.

    Returns
    -------
    (hubs,authorities) : two-tuple of dictionaries
       Two dictionaries keyed by node containing the hub and authority
       values.

    Examples
    --------
    >>> G=nx.path_graph(4)
    >>> h,a=nx.hits(G)

    Notes
    -----
    This implementation uses SciPy sparse matrices.

    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 HITS algorithm was designed for directed graphs but this
    algorithm does not check if the input graph is directed and will
    execute on undirected graphs.

    References
    ----------
    .. [1] A. Langville and C. Meyer,
       "A survey of eigenvector methods of web information retrieval."
       http://citeseer.ist.psu.edu/713792.html
    .. [2] Jon Kleinberg,
       Authoritative sources in a hyperlinked environment
       Journal of the ACM 46 (5): 604-632, 1999.
       doi:10.1145/324133.324140.
       http://www.cs.cornell.edu/home/kleinber/auth.pdf.
    """
    #import sys
    print '\n\t~~~~~~ salsa_scipy (G, max_iter='+str(max_iter)+', tol='+str(tol)+', nstart_dict, normalized='+str(normalized)+') ~~~~~~\n'; sys.stdout.flush()
    try:
        import scipy#.sparse as sp
        import numpy as np
        import sys
    except ImportError:
        raise ImportError(\
            "hits_scipy() requires SciPy: http://scipy.org/")
    if len(G) == 0:
        return {},{}
    print '--- salsa_scipy: ' + str(datetime.now()); sys.stdout.flush(); startTime = datetime.now()      
    ''''M=nx.to_scipy_sparse_matrix(G,nodelist=G.nodes())
    (n,m)=M.shape # should be square
    A=M.T*M # authority matrix'''
    A=get_matrix(G,mat_type='authority',sparse=True,force_ergodicity=True, CN_name=10)
    (n,m)=A.shape # should be square
    if debug:
        new_G_h = nx.DiGraph(A)
        print '\n--- salsa_scipy_old: hub- is new graph stochastic? ' + str(gm.check_if_stochastic_matrix(nx.to_numpy_matrix(new_G_h))); sys.stdout.flush()
        print '--- salsa_scipy_old: hub- is new graph strongly connected? ' + str(nx.is_strongly_connected(new_G_h)); sys.stdout.flush()
        print '--- salsa_scipy_old: hub- is new graph aperiodic? ' + str(nx.is_aperiodic(new_G_h)); sys.stdout.flush()
        new_G_h.clear()
        #print '--- salsa_scipy_old: debug steps (hub) took: '+str(datetime.now()-tmpTime); tmpTime = datetime.now(); sys.stdout.flush()
        
    
    print '--- salsa_scipy: get authority matrix took: ' + str(datetime.now()-startTime); sys.stdout.flush(); tmpTime = datetime.now()      
    
    # choose fixed starting vector if not given
    if nstart_dict is None:
        a=scipy.ones((n,1))/n  # initial guess
    else:
        a=np.asarray(nstart_dict.values()).flatten()       # IN MY CASE: is it the init of hubs or authorities??
        # normalize starting vector
        s=1.0/a.sum()
        for k in a:
            a[k]*=s
            
    # power iteration on authority matrix
    i=0
    a=a.T
#.........这里部分代码省略.........