Python Graph.connected_component_containing_vertex方法代码示例

# 需要导入模块: from sage.graphs.graph import Graph [as 别名]
# 或者: from sage.graphs.graph.Graph import connected_component_containing_vertex [as 别名]
    def cluster_in_box(self, m, pt=None):
        r"""
        Return the cluster (as a list) in the primal box [-m,m]^d
        containing the point pt.

        INPUT:

        - ``m`` - integer
        - ``pt`` - tuple, point in Z^d. If None, pt=zero is considered.

        EXAMPLES::

            sage: from slabbe import BondPercolationSample
            sage: S = BondPercolationSample(0.3,2)
            sage: S.cluster_in_box(2)         # random
            [(-2, -2), (-2, -1), (-1, -2), (-1, -1), (-1, 0), (0, 0)]
        """
        G = Graph()
        G.add_edges(self.edges_in_box(m))
        if pt is None:
            pt = self.zero()
        if pt in G:
            return G.connected_component_containing_vertex(pt)
        else:
            return []

# 需要导入模块: from sage.graphs.graph import Graph [as 别名]
# 或者: from sage.graphs.graph.Graph import connected_component_containing_vertex [as 别名]
def AfricaMap(continental=False, year=2018):
    """
    Return African states as a graph of common border.

    "African state" here is defined as an independent
    state having the capital city in Africa. The graph
    has an edge between those countries that have common
    *land* border.

    INPUT:

    - ``continental``, a Boolean -- if set, only return states in
      the continental Africa
    - ``year`` -- reserved for future use

    EXAMPLES::

        sage: Africa = graphs.AfricaMap(); Africa
        Africa Map: Graph on 54 vertices
        sage: sorted(Africa.neighbors('Libya'))
        ['Algeria', 'Chad', 'Egypt', 'Niger', 'Sudan', 'Tunisia']

        sage: cont_Africa = graphs.AfricaMap(continental=True)
        sage: cont_Africa.order()
        48
        sage: 'Madagaskar' in cont_Africa
        False

    TESTS::

        sage: Africa.plot()
        Graphics object consisting of 159 graphics primitives
    """
    if year != 2018:
        raise ValueError("currently only year 2018 is implemented")

    common_border = {
     'Algeria': ['Libya', 'Mali', 'Mauritania', 'Morocco', 'Niger', 'Tunisia'],
     'Angola': ['Namibia', 'Zambia'],
     'Benin': ['Burkina Faso', 'Niger', 'Nigeria', 'Togo'],
     'Botswana': ['Namibia', 'South Africa', 'Zimbabwe'],
     'Burkina Faso': ['Ghana', 'Ivory Coast', 'Mali', 'Niger', 'Togo'],
     'Cameroon': ['Central Africa', 'Chad', 'Equatorial Guinea', 'Gabon', 'Nigeria'],
     'Central Africa': ['Chad', 'South Sudan', 'Sudan'],
     'Chad': ['Libya', 'Niger', 'Nigeria', 'Sudan'],
     'Republic of the Congo': ['Gabon', 'Cameroon', 'Central Africa', 'Angola',
                               'Democratic Republic of the Congo'],
     'Democratic Republic of the Congo': ['Zambia', 'South Sudan', 'Tanzania', 'Burundi',
                                          'Rwanda', 'Uganda', 'Central Africa', 'Angola'],
     'Djibouti': ['Eritrea', 'Ethiopia', 'Somalia'],
     'Ethiopia': ['Eritrea', 'Kenya', 'Somalia', 'South Sudan', 'Sudan'],
     'Gabon': ['Equatorial Guinea'],
     'Ghana': ['Ivory Coast', 'Togo'],
     'Guinea': ['Guinea-Bissau', 'Ivory Coast', 'Liberia', 'Sierra Leone'],
     'Kenya': ['Somalia', 'South Sudan', 'Tanzania', 'Uganda'],
     'Liberia': ['Ivory Coast', 'Sierra Leone'],
     'Libya': ['Egypt', 'Niger', 'Sudan', 'Tunisia'],
     'Mali': ['Guinea', 'Ivory Coast', 'Mauritania', 'Niger', 'Senegal'],
     'Mozambique': ['Malawi', 'South Africa', 'Swaziland', 'Zimbabwe'],
     'Niger': ['Nigeria'],
     'Rwanda': ['Burundi', 'Tanzania', 'Uganda'],
     'Senegal': ['Guinea', 'Guinea-Bissau', 'Mauritania', 'Gambia'],
     'South Africa': ['Lesotho', 'Namibia', 'Swaziland', 'Zimbabwe'],
     'South Sudan': ['Uganda', 'Sudan', 'Democratic Republic of the Congo'],
     'Sudan': ['Egypt', 'Eritrea'],
     'Tanzania': ['Burundi', 'Malawi', 'Mozambique', 'Uganda', 'Zambia'],
     'Zambia': ['Malawi', 'Mozambique', 'Namibia', 'Zimbabwe']
     }

    no_land_border = ['Cape Verde', 'Seychelles', 'Mauritius', u'São Tomé and Príncipe', 'Madagascar', 'Comoros']

    G = Graph(common_border, format='dict_of_lists')

    if continental:
        G = G.subgraph(G.connected_component_containing_vertex('Central Africa'))
        G.name(new="Continental Africa Map")
    else:
        G.add_vertices(no_land_border)
        G.name(new="Africa Map")

    return G

# 需要导入模块: from sage.graphs.graph import Graph [as 别名]
# 或者: from sage.graphs.graph.Graph import connected_component_containing_vertex [as 别名]
def EuropeMap(continental=False, year=2018):
    """
    Return European states as a graph of common border.

    "European state" here is defined as an independent
    state having the capital city in Europe. The graph
    has an edge between those countries that have common
    *land* border.

    INPUT:

    - ``continental``, a Boolean -- if set, only return states in
      the continental Europe
    - ``year`` -- reserved for future use

    EXAMPLES::

        sage: Europe = graphs.EuropeMap(); Europe
        Europe Map: Graph on 44 vertices
        sage: Europe.neighbors('Ireland')
        ['United Kingdom']

        sage: cont_Europe = graphs.EuropeMap(continental=True)
        sage: cont_Europe.order()
        40
        sage: 'Iceland' in cont_Europe
        False
    """
    if year != 2018:
        raise ValueError("currently only year 2018 is implemented")

    common_border = {
     'Poland': ['Slovakia', 'Czech Republic', 'Lithuania', 'Russia', 'Ukraine', 'Germany'],
     'Germany': ['Czech Republic', 'Netherlands', 'Switzerland', 'Luxembourg', 'Denmark'],
     'Croatia': ['Bosnia and Herzegovina', 'Serbia', 'Hungary', 'Montenegro', 'Slovenia'],
     'Austria': ['Czech Republic', 'Germany', 'Switzerland', 'Slovenia', 'Liechtenstein'],
     'France': ['Germany', 'Italy', 'Switzerland', 'Monaco', 'Luxembourg', 'Andorra'],
     'Hungary': ['Slovakia', 'Serbia', 'Romania', 'Ukraine', 'Slovenia', 'Austria'],
     'Italy': ['Switzerland', 'Vatican City', 'San Marino', 'Slovenia', 'Austria'],
     'Belarus': ['Poland', 'Latvia', 'Lithuania', 'Russia', 'Ukraine'],
     'Montenegro': ['Bosnia and Herzegovina', 'Serbia', 'Albania'],
     'Belgium': ['Germany', 'Netherlands', 'Luxembourg', 'France'],
     'Russia': ['Finland', 'Lithuania', 'Estonia', 'Ukraine'],
     'Romania': ['Serbia', 'Moldova', 'Bulgaria', 'Ukraine'],
     'Latvia': ['Lithuania', 'Russia', 'Estonia'],
     'Slovakia': ['Czech Republic', 'Ukraine', 'Austria'], 'Switzerland': ['Liechtenstein'],
     'Spain': ['Portugal', 'Andorra', 'France'], 'Norway': ['Finland', 'Sweden', 'Russia'],
     'Ireland': ['United Kingdom'], 'Serbia': ['Bosnia and Herzegovina', 'Bulgaria'],
     'Greece': ['Macedonia', 'Bulgaria', 'Albania'], 'Ukraine': ['Moldova'],
     'Macedonia': ['Serbia', 'Bulgaria', 'Albania'], 'Sweden': ['Finland']
    }
    no_land_border = ['Iceland', 'Malta']

    G = Graph(common_border, format='dict_of_lists')

    if continental:
        G = G.subgraph(G.connected_component_containing_vertex('Austria'))
        G.name(new="Continental Europe Map")
    else:
        G.add_vertices(no_land_border)
        G.name(new="Europe Map")

    return G