Python networkx.caveman_graph() Examples

def caveman_special(c=2,k=20,p_path=0.1,p_edge=0.3):
    p = p_path
    path_count = max(int(np.ceil(p * k)),1)
    G = nx.caveman_graph(c, k)
    # remove 50% edges
    p = 1-p_edge
    for (u, v) in list(G.edges()):
        if np.random.rand() < p and ((u < k and v < k) or (u >= k and v >= k)):
            G.remove_edge(u, v)
    # add path_count links
    for i in range(path_count):
        u = np.random.randint(0, k)
        v = np.random.randint(k, k * 2)
        G.add_edge(u, v)
    G = max(nx.connected_component_subgraphs(G), key=len)
    return G 

def caveman_special(c=2,k=20,p_path=0.1,p_edge=0.3):
    p = p_path
    path_count = max(int(np.ceil(p * k)),1)
    G = nx.caveman_graph(c, k)
    # remove 50% edges
    p = 1-p_edge
    for (u, v) in list(G.edges()):
        if np.random.rand() < p and ((u < k and v < k) or (u >= k and v >= k)):
            G.remove_edge(u, v)
    # add path_count links
    for i in range(path_count):
        u = np.random.randint(0, k)
        v = np.random.randint(k, k * 2)
        G.add_edge(u, v)
    G = max(nx.connected_component_subgraphs(G), key=len)
    return G 

def caveman_special(c=2,k=20,p_path=0.1,p_edge=0.3):
    p = p_path
    path_count = max(int(np.ceil(p * k)),1)
    G = nx.caveman_graph(c, k)
    # remove 50% edges
    p = 1-p_edge
    for (u, v) in list(G.edges()):
        if np.random.rand() < p and ((u < k and v < k) or (u >= k and v >= k)):
            G.remove_edge(u, v)
    # add path_count links
    for i in range(path_count):
        u = np.random.randint(0, k)
        v = np.random.randint(k, k * 2)
        G.add_edge(u, v)
    G = max(nx.connected_component_subgraphs(G), key=len)
    return G 

def test_caveman_graph():
    G = nx.caveman_graph(4,3)
    assert_equal(len(G),12)
    assert_equal(len(G.nodes()),12)
    
    G = nx.caveman_graph(1,5)
    K5 = nx.complete_graph(5)
    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_caveman_graph():
    G = nx.caveman_graph(4, 3)
    assert_equal(len(G), 12)

    G = nx.caveman_graph(1, 5)
    K5 = nx.complete_graph(5)
    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_caveman_graph():
    G = nx.caveman_graph(4, 3)
    assert_equal(len(G), 12)

    G = nx.caveman_graph(1, 5)
    K5 = nx.complete_graph(5)
    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 relaxed_caveman_graph(l, k, p, seed=None):
    """Return a relaxed caveman graph.

    A relaxed caveman graph starts with ``l`` cliques of size ``k``.  Edges are
    then randomly rewired with probability ``p`` to link different cliques.

    Parameters
    ----------
    l : int
      Number of groups
    k : int
      Size of cliques
    p : float
      Probabilty of rewiring each edge.
    seed : int,optional
      Seed for random number generator(default=None)

    Returns
    -------
    G : NetworkX Graph
      Relaxed Caveman Graph

    Raises
    ------
    NetworkXError:
     If p is not in [0,1]

    Examples
    --------
    >>> G = nx.relaxed_caveman_graph(2, 3, 0.1, seed=42)

    References
    ----------
    .. [1] Santo Fortunato, Community Detection in Graphs,
       Physics Reports Volume 486, Issues 3-5, February 2010, Pages 75-174.
       http://arxiv.org/abs/0906.0612
    """
    if not seed is None:
        random.seed(seed)
    G = nx.caveman_graph(l, k)
    nodes = G.nodes()
    G.name = "relaxed_caveman_graph (%s,%s,%s)" % (l, k, p)
    for (u, v) in G.edges():
        if random.random() < p:  # rewire the edge
            x = random.choice(nodes)
            if G.has_edge(u, x):
                continue
            G.remove_edge(u, v)
            G.add_edge(u, x)
    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 relaxed_caveman_graph(l, k, p, seed=None):
    """Returns a relaxed caveman graph.

    A relaxed caveman graph starts with `l` cliques of size `k`.  Edges are
    then randomly rewired with probability `p` to link different cliques.

    Parameters
    ----------
    l : int
      Number of groups
    k : int
      Size of cliques
    p : float
      Probabilty of rewiring each edge.
    seed : integer, random_state, or None (default)
        Indicator of random number generation state.
        See :ref:`Randomness<randomness>`.

    Returns
    -------
    G : NetworkX Graph
      Relaxed Caveman Graph

    Raises
    ------
    NetworkXError:
     If p is not in [0,1]

    Examples
    --------
    >>> G = nx.relaxed_caveman_graph(2, 3, 0.1, seed=42)

    References
    ----------
    .. [1] Santo Fortunato, Community Detection in Graphs,
       Physics Reports Volume 486, Issues 3-5, February 2010, Pages 75-174.
       https://arxiv.org/abs/0906.0612
    """
    G = nx.caveman_graph(l, k)
    nodes = list(G)
    for (u, v) in G.edges():
        if seed.random() < p:  # rewire the edge
            x = seed.choice(nodes)
            if G.has_edge(u, x):
                continue
            G.remove_edge(u, v)
            G.add_edge(u, x)
    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 relaxed_caveman_graph(l, k, p, seed=None):
    """Return a relaxed caveman graph.

    A relaxed caveman graph starts with `l` cliques of size `k`.  Edges are
    then randomly rewired with probability `p` to link different cliques.

    Parameters
    ----------
    l : int
      Number of groups
    k : int
      Size of cliques
    p : float
      Probabilty of rewiring each edge.
    seed : int,optional
      Seed for random number generator(default=None)

    Returns
    -------
    G : NetworkX Graph
      Relaxed Caveman Graph

    Raises
    ------
    NetworkXError:
     If p is not in [0,1]

    Examples
    --------
    >>> G = nx.relaxed_caveman_graph(2, 3, 0.1, seed=42)

    References
    ----------
    .. [1] Santo Fortunato, Community Detection in Graphs,
       Physics Reports Volume 486, Issues 3-5, February 2010, Pages 75-174.
       https://arxiv.org/abs/0906.0612
    """
    if seed is not None:
        random.seed(seed)
    G = nx.caveman_graph(l, k)
    nodes = list(G)
    for (u, v) in G.edges():
        if random.random() < p:  # rewire the edge
            x = random.choice(nodes)
            if G.has_edge(u, x):
                continue
            G.remove_edge(u, v)
            G.add_edge(u, x)
    return G