Python networkx.connected_caveman_graph() Examples

def test_encode_decode_adj():
######## code test ###########
    G = nx.ladder_graph(5)
    G = nx.grid_2d_graph(20,20)
    G = nx.ladder_graph(200)
    G = nx.karate_club_graph()
    G = nx.connected_caveman_graph(2,3)
    print(G.number_of_nodes())
    
    adj = np.asarray(nx.to_numpy_matrix(G))
    G = nx.from_numpy_matrix(adj)
    #
    start_idx = np.random.randint(adj.shape[0])
    x_idx = np.array(bfs_seq(G, start_idx))
    adj = adj[np.ix_(x_idx, x_idx)]
    
    print('adj\n',adj)
    adj_output = encode_adj(adj,max_prev_node=5)
    print('adj_output\n',adj_output)
    adj_recover = decode_adj(adj_output,max_prev_node=5)
    print('adj_recover\n',adj_recover)
    print('error\n',np.amin(adj_recover-adj),np.amax(adj_recover-adj))
    
    
    adj_output = encode_adj_flexible(adj)
    for i in range(len(adj_output)):
        print(len(adj_output[i]))
    adj_recover = decode_adj_flexible(adj_output)
    print(adj_recover)
    print(np.amin(adj_recover-adj),np.amax(adj_recover-adj)) 

def test_encode_decode_adj():
######## code test ###########
    G = nx.ladder_graph(5)
    G = nx.grid_2d_graph(20,20)
    G = nx.ladder_graph(200)
    G = nx.karate_club_graph()
    G = nx.connected_caveman_graph(2,3)
    print(G.number_of_nodes())
    
    adj = np.asarray(nx.to_numpy_matrix(G))
    G = nx.from_numpy_matrix(adj)
    #
    start_idx = np.random.randint(adj.shape[0])
    x_idx = np.array(bfs_seq(G, start_idx))
    adj = adj[np.ix_(x_idx, x_idx)]
    
    print('adj\n',adj)
    adj_output = encode_adj(adj,max_prev_node=5)
    print('adj_output\n',adj_output)
    adj_recover = decode_adj(adj_output,max_prev_node=5)
    print('adj_recover\n',adj_recover)
    print('error\n',np.amin(adj_recover-adj),np.amax(adj_recover-adj))
    
    
    adj_output = encode_adj_flexible(adj)
    for i in range(len(adj_output)):
        print(len(adj_output[i]))
    adj_recover = decode_adj_flexible(adj_output)
    print(adj_recover)
    print(np.amin(adj_recover-adj),np.amax(adj_recover-adj)) 

def test_connected_caveman_graph():
    G = nx.connected_caveman_graph(4,3)
    assert_equal(len(G),12)
    assert_equal(len(G.nodes()),12)
    
    G = nx.connected_caveman_graph(1,5)
    K5 = nx.complete_graph(5)
    K5.remove_edge(3,4)
    assert_true(nx.is_isomorphic(G,K5)) 

def connected_caveman_graph(l, k):
    """Returns a connected caveman graph of `l` cliques of size `k`.

    The connected caveman graph is formed by creating `n` cliques of size
    `k`, then a single edge in each clique is rewired to a node in an
    adjacent clique.

    Parameters
    ----------
    l : int
      number of cliques
    k : int
      size of cliques

    Returns
    -------
    G : NetworkX Graph
      connected caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.connected_caveman_graph(3, 3)

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    G = nx.caveman_graph(l, k)
    for start in range(0, l * k, k):
        G.remove_edge(start, start + 1)
        G.add_edge(start, (start - 1) % (l * k))
    return G 

def test_connected_caveman_graph():
    G = nx.connected_caveman_graph(4, 3)
    assert_equal(len(G), 12)

    G = nx.connected_caveman_graph(1, 5)
    K5 = nx.complete_graph(5)
    K5.remove_edge(3, 4)
    assert_true(nx.is_isomorphic(G, K5)) 

def connected_caveman_graph(l, k):
    """Returns a connected caveman graph of `l` cliques of size `k`.

    The connected caveman graph is formed by creating `n` cliques of size
    `k`, then a single edge in each clique is rewired to a node in an
    adjacent clique.

    Parameters
    ----------
    l : int
      number of cliques
    k : int
      size of cliques

    Returns
    -------
    G : NetworkX Graph
      connected caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.connected_caveman_graph(3, 3)

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    G = nx.caveman_graph(l, k)
    for start in range(0, l * k, k):
        G.remove_edge(start, start + 1)
        G.add_edge(start, (start - 1) % (l * k))
    return G 

def test_connected_caveman_graph():
    G = nx.connected_caveman_graph(4, 3)
    assert_equal(len(G), 12)

    G = nx.connected_caveman_graph(1, 5)
    K5 = nx.complete_graph(5)
    K5.remove_edge(3, 4)
    assert_true(nx.is_isomorphic(G, K5)) 

def caveman_graph(l, k):
    """Returns a caveman graph of ``l`` cliques of size ``k``.

    Parameters
    ----------
    l : int
      Number of cliques
    k : int
      Size of cliques

    Returns
    -------
    G : NetworkX Graph
      caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.caveman_graph(3, 3)

    See also
    --------

    connected_caveman_graph

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    # l disjoint cliques of size k
    G = nx.empty_graph(l*k)
    G.name = "caveman_graph(%s,%s)" % (l*k, k)
    if k > 1:
        for start in range(0, l*k, k):
            edges = itertools.combinations(range(start, start+k), 2)
            G.add_edges_from(edges)
    return G 

def connected_caveman_graph(l, k):
    """Returns a connected caveman graph of ``l`` cliques of size ``k``.

    The connected caveman graph is formed by creating ``n`` cliques of size
    ``k``, then a single edge in each clique is rewired to a node in an
    adjacent clique.

    Parameters
    ----------
    l : int
      number of cliques
    k : int
      size of cliques

    Returns
    -------
    G : NetworkX Graph
      connected caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.connected_caveman_graph(3, 3)

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    G = nx.caveman_graph(l, k)
    G.name = "connected_caveman_graph(%s,%s)" % (l, k)
    for start in range(0, l*k, k):
        G.remove_edge(start, start+1)
        G.add_edge(start, (start-1) % (l*k))
    return G 

def caveman_graph(l, k):
    """Returns a caveman graph of `l` cliques of size `k`.

    Parameters
    ----------
    l : int
      Number of cliques
    k : int
      Size of cliques

    Returns
    -------
    G : NetworkX Graph
      caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.caveman_graph(3, 3)

    See also
    --------

    connected_caveman_graph

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    # l disjoint cliques of size k
    G = nx.empty_graph(l * k)
    if k > 1:
        for start in range(0, l * k, k):
            edges = itertools.combinations(range(start, start + k), 2)
            G.add_edges_from(edges)
    return G 

def ring_of_cliques(num_cliques, clique_size):
    """Defines a "ring of cliques" graph.

    A ring of cliques graph is consisting of cliques, connected through single
    links. Each clique is a complete graph.

    Parameters
    ----------
    num_cliques : int
        Number of cliques
    clique_size : int
        Size of cliques

    Returns
    -------
    G : NetworkX Graph
        ring of cliques graph

    Raises
    ------
    NetworkXError
        If the number of cliques is lower than 2 or
        if the size of cliques is smaller than 2.

    Examples
    --------
    >>> G = nx.ring_of_cliques(8, 4)

    See Also
    --------
    connected_caveman_graph

    Notes
    -----
    The `connected_caveman_graph` graph removes a link from each clique to
    connect it with the next clique. Instead, the `ring_of_cliques` graph
    simply adds the link without removing any link from the cliques.
    """
    if num_cliques < 2:
        raise nx.NetworkXError('A ring of cliques must have at least '
                               'two cliques')
    if clique_size < 2:
        raise nx.NetworkXError('The cliques must have at least two nodes')

    G = nx.Graph()
    for i in range(num_cliques):
        edges = itertools.combinations(range(i * clique_size, i * clique_size +
                                             clique_size), 2)
        G.add_edges_from(edges)
        G.add_edge(i * clique_size + 1, (i + 1) * clique_size %
                   (num_cliques * clique_size))
    return G 

def caveman_graph(l, k):
    """Returns a caveman graph of `l` cliques of size `k`.

    Parameters
    ----------
    l : int
      Number of cliques
    k : int
      Size of cliques

    Returns
    -------
    G : NetworkX Graph
      caveman graph

    Notes
    -----
    This returns an undirected graph, it can be converted to a directed
    graph using :func:`nx.to_directed`, or a multigraph using
    ``nx.MultiGraph(nx.caveman_graph(l, k))``. Only the undirected version is
    described in [1]_ and it is unclear which of the directed
    generalizations is most useful.

    Examples
    --------
    >>> G = nx.caveman_graph(3, 3)

    See also
    --------

    connected_caveman_graph

    References
    ----------
    .. [1] Watts, D. J. 'Networks, Dynamics, and the Small-World Phenomenon.'
       Amer. J. Soc. 105, 493-527, 1999.
    """
    # l disjoint cliques of size k
    G = nx.empty_graph(l * k)
    if k > 1:
        for start in range(0, l * k, k):
            edges = itertools.combinations(range(start, start + k), 2)
            G.add_edges_from(edges)
    return G 

def ring_of_cliques(num_cliques, clique_size):
    """Defines a "ring of cliques" graph.

    A ring of cliques graph is consisting of cliques, connected through single
    links. Each clique is a complete graph.

    Parameters
    ----------
    num_cliques : int
      Number of cliques
    clique_size : int
      Size of cliques

    Returns
    -------
    G : NetworkX Graph
      ring of cliques graph

    Raises
    ------
    NetworkXError
        If the number of cliques is lower than 2 or
        if the size of cliques is smaller than 2.

    Examples
    --------
    >>> G = nx.ring_of_cliques(8, 4)

    See Also
    --------
    connected_caveman_graph

    Notes
    -----
    The `connected_caveman_graph` graph removes a link from each clique to
    connect it with the next clique. Instead, the `ring_of_cliques` graph
    simply adds the link without removing any link from the cliques.
    """
    if num_cliques < 2:
        raise nx.NetworkXError('A ring of cliques must have at least '
                               'two cliques')
    if clique_size < 2:
        raise nx.NetworkXError('The cliques must have at least two nodes')

    G = nx.Graph()
    for i in range(num_cliques):
        edges = itertools.combinations(range(i * clique_size, i * clique_size +
                                             clique_size), 2)
        G.add_edges_from(edges)
        G.add_edge(i * clique_size + 1, (i + 1) * clique_size %
                   (num_cliques * clique_size))
    return G