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classic.py

00001 """
Generators for some classic graphs.

The typical graph generator is called as follows:

>>> G=complete_graph(100)

returning the complete graph on n nodes labeled 0,..,99
as a simple graph. Except for empty_graph, all the generators 
in this module return a Graph class (i.e. a simple, undirected graph).

"""
#    Copyright (C) 2004,2005 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    Distributed under the terms of the GNU Lesser General Public License
#    http://www.gnu.org/copyleft/lesser.html
__author__ ="""Aric Hagberg (hagberg@lanl.gov)\nPieter Swart (swart@lanl.gov)"""
__date__ = "$Date: 2005-06-17 14:06:03 -0600 (Fri, 17 Jun 2005) $"
__credits__ = """"""
__revision__ = "$Revision: 1056 $"


#-------------------------------------------------------------------
#   Some Classic Graphs
#-------------------------------------------------------------------
import networkx


00031 def balanced_tree(r,h):
    """Return the perfectly balanced r-tree of height h.

    For r>=2, h>=1, this is the rooted tree where all leaves
    are at distance h from the root.
    The root has degree r and all other internal nodes have degree r+1.

    number_of_nodes = 1+r+r**2+...+r**h = (r**(h+1)-1)/(r-1), 
    number_of_edges = number_of_nodes - 1.

    Node labels are the integers 0 (the root) up to 
    number_of_nodes - 1.
    
    """
    if r<2:
        raise networkx.NetworkXError, \
              "Invalid graph description, r should be >=2"
    if h<1:
        raise networkx.NetworkXError, \
              "Invalid graph description, h should be >=1"
    
    G=empty_graph()
    G.name="balanced_tree(%d,%d)"%(r,h)

    # Grow tree of increasing height by repeatedly adding a layer
    # of new leaves to current leaves.
    
    # First create root of degree r
    root=0
    v=root
    G.add_node(v)
    newleavelist=[]
    i=0
    while i < r:
        v=v+1
        G.add_edge(root,v)
        newleavelist.append(v)
        i=i+1
    # All other  internal nodes have degree r+1
    height=1
    while height<h:
        leavelist=newleavelist[:]
        newleavelist=[]
        for leave in leavelist:
            for i in xrange(r):
                v=v+1
                G.add_edge(leave,v)
                newleavelist.append(v)
        height=height+1
    return G

00082 def barbell_graph(m1,m2):
    """Return the Barbell Graph: two complete graphs connected by a path.

    For m1 > 1 and m2 >= 0.

    Two identical complete graphs K_{m1} form the left and right bells,
    and are connected by a path P_{m2}.

    The 2*m1+m2  nodes are numbered
        0,...,m1-1 for the left barbell,
        m1,...,m1+m2-1 for the path,
        and m1+m2,...,2*m1+m2-1 for the right barbell.

    The 3 subgraphs are joined via the edges (m1-1,m1) and (m1+m2-1,m1+m2).
    If m2=0, this is merely two complete graphs joined together.

    This graph is an extremal example in David Aldous
    and Jim Fill's etext on Random Walks on Graphs.

    """
    if m1<2:
        raise networkx.NetworkXError, \
              "Invalid graph description, m1 should be >=2"
    if m2<0:
        raise networkx.NetworkXError, \
              "Invalid graph description, m2 should be >=0"

    # left barbell
    G=complete_graph(m1)
    G.name="barbell_graph(%d,%d)"%(m1,m2)
    
    # connecting path
    G.add_nodes_from([v for v in range(m1,m1+m2-1)])
    if m2>1:
        G.add_edges_from([(v,v+1) for v in range(m1,m1+m2-1)])
    # right barbell
    for u in range(m1+m2,2*m1+m2):
        for v in range(u,2*m1+m2):
            G.add_edge(u,v)
    # connect it up
    G.add_edge(m1-1,m1)
    if m2>0:
        G.add_edge(m1+m2-1,m1+m2)
    return G

00127 def complete_graph(n,create_using=None):
    """ Return the Complete graph K_n with n nodes. 
    
    Node labels are the integers 0 to n-1.

    """
    G=empty_graph(n,create_using)
    G.name="complete_graph(%d)"%n
    for u in xrange(n):
        for v in xrange(u,n):
            G.add_edge(u,v)
    return G

00140 def complete_bipartite_graph(n1,n2):
    """Return the complete bipartite graph K_{n1_n2}.
    
    Composed of two partitions with n1 nodes in the first 
    and n2 nodes in the second. Each node in the first is 
    connected to each node in the second.

    Node labels are the integers 0 to n1+n2-1
    
    """
    G=empty_graph(n1+n2)
    G.name="complete_bipartite_graph(%d,%d)"%(n1,n2)
    for v1 in xrange(n1):
        for v2 in xrange(n2):
            G.add_edge(v1,n1+v2)
    return G

00157 def circular_ladder_graph(n):
    """Return the circular ladder graph CL_n of length n.

    CL_n consists of two concentric n-cycles in which
    each of the n pairs of concentric nodes are joined by an edge.

    Node labels are the integers 0 to n-1
    
    """
    G=ladder_graph(n)
    G.name="circular_ladder_graph(%d)"%n
    G.add_edge(0,n-1)
    G.add_edge(n,2*n-1)
    return G

00172 def cycle_graph(n,create_using=None):
    """Return the cycle graph C_n over n nodes.
   
    C_n is the n-path with two end-nodes connected.

    Node labels are the integers 0 to n-1
    If create_using is a DiGraph, the direction is in increasing order.
    
    """
    G=path_graph(n,create_using)
    G.name="cycle_graph(%d)"%n
    if n>1: G.add_edge(n-1,0)
    return G

00186 def dorogovtsev_goltsev_mendes_graph(n):
    """Return the hierarchically constructed Dorogovtsev-Goltsev-Mendes graph.

    n is the generation.
    See: arXiv:/cond-mat/0112143 by Dorogovtsev, Goltsev and Mendes.
    
    """
    G=networkx.Graph()
    G.name="Dorogovtsev-Goltsev-Mendes Graph"
    G.add_edge(0,1)
    if n==0:
        return G
    new_node = 2         # next node to be added
    for i in range(1,n+1): #iterate over number of generations.
        last_generation_edges = G.edges()
        number_of_edges_in_last_generation = len(last_generation_edges)
        for j in range(0,number_of_edges_in_last_generation):
            G.add_edge(new_node,last_generation_edges[j][0])
            G.add_edge(new_node,last_generation_edges[j][1])
            new_node += 1
    return G

00208 def empty_graph(n=0,create_using=None):
    """Return the empty graph with n nodes and zero edges.

    Node labels are the integers 0 to n-1

    For example:
    >>> from networkx import *
    >>> G=empty_graph(10)
    >>> G.number_of_nodes()
    10
    >>> G.number_of_edges()
    0
 
    The variable create_using should point to a "graph"-like object that
    will be cleaned (nodes and edges will be removed) and refitted as
    an empty "graph" with n nodes with integer labels. This capability
    is useful for specifying the class-nature of the resulting empty
    "graph" (i.e. Graph, DiGraph, MyWeirdGraphClass, etc.).
    
    The variable create_using has two main uses:
    Firstly, the variable create_using can be used to create an
    empty digraph, network,etc.  For example,

    >>> n=10
    >>> G=empty_graph(n,create_using=DiGraph())

    will create an empty digraph on n nodes.

    Secondly, one can pass an existing graph (digraph, pseudograph,
    etc.) via create_using. For example, if G is an existing graph
    (resp. digraph, pseudograph, etc.), then empty_graph(n,create_using=G)
    will empty G (i.e. delete all nodes and edges using G.clear() in
    base) and then add n nodes and zero edges, and return the modified
    graph (resp. digraph, pseudograph, etc.).

    WARNING: The graph dna is not scrubbed in this process.

    See also create_empty_copy(G).
    
    """
    if create_using is None:
        # default empty graph is a simple graph
        G=networkx.Graph()
    else:
        G=create_using
        G.clear()

    G.add_nodes_from(xrange(n))
    G.name="empty_graph(%d)"%n 
    return G

00259 def grid_2d_graph(m,n,periodic=False):
    """ Return the 2d grid graph of mxn nodes,
        each connected to its nearest neighbors.
        Optional argument periodic=True will connect
        boundary nodes via periodic boundary conditions.
    """
    G=empty_graph()
    G.name="grid 2d graph"
    rows=range(m)
    columns=range(n)
    def _label(i,j):
        return (i,j)
    for i in rows:
        for j in columns:
            G.add_node( _label(i,j) )
    for i in rows:
        for j in columns:
            if i>0: G.add_edge( _label(i,j), _label(i-1,j) )
            if i<m-1: G.add_edge( _label(i,j), _label(i+1,j) )
            if j>0: G.add_edge( _label(i,j), _label(i,j-1) )
            if j<n-1: G.add_edge( _label(i,j), _label(i,j+1) )
    if periodic:
        for i in rows:
            G.add_edge(_label(i,0), _label(i,n-1))
        for j in columns:
            G.add_edge(_label(0,j), _label(m-1,j))
        G.name="periodic_grid_2d_graph(%d,%d)"%(m,n)
    return G


00289 def grid_graph(dim,periodic=False):
    """ Return the n-dimensional grid graph.

    The dimension is the length of the list 'dim' and the
    size in each dimension is the value of the list element.

    E.g. G=grid_graph(dim=[2,3]) produces a 2x3 grid graph.

    If periodic=True then join grid edges with periodic boundary conditions.

    """    
    from networkx.utils import is_list_of_ints
    dlabel="%s"%dim
    if dim==[]:
        G=networkx.Graph()
        G.name="grid_graph(%s)"%dim
        return G
    if not is_list_of_ints(dim):
        raise networkx.NetworkXError,"dim is not a list of integers"
    if min(dim)<=0:
        raise networkx.NetworkXError,\
              "dim is not a list of strictly positive integers"       
    if periodic:
        func=cycle_graph
    else:
        func=path_graph

    current_dim=dim.pop()
    G=func(current_dim)
    while len(dim)>0:
        current_dim=dim.pop() 
        Gnew=func(current_dim)
        Gold=G.copy()
        G=networkx.operators.cartesian_product(Gnew,Gold)
    # graph G is done but has labels of the form (1,(2,(3,1)))
    # so relabel
    H=networkx.operators.relabel_nodes(G, networkx.utils.flatten)
    H.name="grid_graph(%s)"%dlabel
    return H

00329 def hypercube_graph(n):
    """Return the n-dimensional hypercube.

    Node labels are the integers 0 to 2**n - 1.

    """
    dim=n*[2]
    G=grid_graph(dim)
    G.name="hypercube_graph_(%d)"%n
    return G

00340 def ladder_graph(n):
    """Return the Ladder graph of length n.

    This is two rows of n nodes, with
    each pair connected by a single edge.

    Node labels are the integers 0 to 2*n - 1.
    
    """
    G=empty_graph(2*n)
    G.name="ladder_graph_(%d)"%n 
    G.add_edges_from([(v,v+1) for v in xrange(n-1)])
    G.add_edges_from([(v,v+1) for v in xrange(n,2*n-1)])
    G.add_edges_from([(v,v+n) for v in xrange(n)])
    return G

00356 def lollipop_graph(m,n):
    """Return the Lollipop Graph; K_m connected to P_n.

    This is the Barbell Graph without the right barbell.

    For m>1 and n>=0, the complete graph K_m is connected to the 
    path P_n.  The resulting m+n nodes are labelled 0,...,m-1 for the
    complete graph and m,...,m+n-1 for the path. The 2 subgraphs
    are joined via the edge (m-1,m).  If n=0, this is merely a complete 
    graph.

    Node labels are the integers 0 to number_of_nodes - 1.

    (This graph is an extremal example in David Aldous and Jim
    Fill's etext on Random Walks on Graphs.)
    
    """
    if m<2:
        raise networkx.NetworkXError, \
              "Invalid graph description, m should be >=2"
    if n<0:
        raise networkx.NetworkXError, \
              "Invalid graph description, n should be >=0"
    # the ball
    G=complete_graph(m)
    # the stick
    G.add_nodes_from([v for v in xrange(m,m+n)])
    if n>1:
        G.add_edges_from([(v,v+1) for v in xrange(m,m+n-1)])
    # connect ball to stick
    if m>0: G.add_edge(m-1,m)
    G.name="lollipop_graph(%d,%d)"%(m,n)
    return G

00390 def null_graph(create_using=None):
    """ Return the Null graph with no nodes or edges. 

    See empty_graph for the use of create_using.

    """
    G=empty_graph(0,create_using)
    G.name="null_graph()"
    return G

00400 def path_graph(n,create_using=None):
    """Return the Path graph P_n of n nodes linearly connected
    by n-1 edges.

    Node labels are the integers 0 to n - 1.
    If create_using is a DiGraph then the edges are directed in 
    increasing order.

    """
    G=empty_graph(n,create_using)
    G.name="path_graph(%d)"%n
    G.add_edges_from([(v,v+1) for v in xrange(n-1)])
    return G

00414 def star_graph(n):
    """ Return the Star graph with n+1 nodes:
    one center node, connected to n outer nodes.

   Node labels are the integers 0 to n.

    """
    G=complete_bipartite_graph(1,n)
    G.name="star_graph(%d)"%n
    return G

00425 def trivial_graph():
    """ Return the Trivial graph with one node (with integer label 0)
    and no edges.

    """
    G=empty_graph(1)
    G.name="trivial_graph()"
    return G

00434 def wheel_graph(n):
    """ Return the wheel graph: a single hub node connected
    to each node of the (n-1)-node cycle graph. 

   Node labels are the integers 0 to n - 1.

    """
    G=star_graph(n-1)
    G.name="wheel_graph(%d)"%n
    G.add_edges_from([(v,v+1) for v in xrange(1,n-1)])
    if n>1:
        G.add_edge(1,n-1)
    return G
                        

def _test_suite():
    import doctest
    suite = doctest.DocFileSuite('tests/generators/classic.txt',
                                 package='networkx')
    return suite


if __name__ == "__main__":
    import os
    import sys
    import unittest
    if sys.version_info[:2] < (2, 4):
        print "Python version 2.4 or later required (%d.%d detected)."\
              %  sys.version_info[:2]
        sys.exit(-1)
    # directory of networkx package (relative to this)
    nxbase=sys.path[0]+os.sep+os.pardir
    sys.path.insert(0,nxbase) # prepend to search path
    unittest.TextTestRunner().run(_test_suite())
    

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