"""
Graph database
INFO:
This module implements classes (GraphDatabase, GraphQuery,
GenericGraphQuery) for interfacing with the sqlite database
graphs.db.
The GraphDatabase class interfaces with the sqlite database
graphs.db. It is an immutable database that inherits from
SQLDatabase (see sage.databases.database.py).
The database contains all unlabeled graphs with 7 or fewer nodes.
This class will also interface with the optional database package
containing all unlabeled graphs with 8 or fewer nodes. The
database(s) consists of five tables, and has the structure given by
the function graph_info. (For a full description including column
data types, create a GraphDatabase instance and call the method
get_skeleton).
AUTHORS:
- Emily A. Kirkman (2008-09-20): first version of interactive queries,
cleaned up code and generalized many elements to
sage.databases.database.py
- Emily A. Kirkman (2007-07-23): inherits GenericSQLDatabase, also
added classes: GraphQuery and GenericGraphQuery
- Emily A. Kirkman (2007-05-11): initial sqlite version
- Emily A. Kirkman (2007-02-13): initial version (non-sqlite)
REFERENCES:
- Data provided by Jason Grout (Brigham Young University). [Online]
Available: http://math.byu.edu/~grout/graphs/
"""
import graph
import re
from sage.rings.integer import Integer
from sqlite3 import dbapi2 as sqlite
from sage.databases.sql_db import SQLDatabase, SQLQuery
from sage.misc.misc import SAGE_DATA
from sage.graphs.graph import Graph
dblocation = SAGE_DATA + '/graphs/graphs.db'
def degseq_to_data(degree_sequence):
"""
Takes a degree sequence list (of Integers) and converts to a sorted
(max-min) integer data type, as used for faster access in the
underlying database.
EXAMPLE::
sage: from sage.graphs.graph_database import degseq_to_data
sage: degseq_to_data([2,2,3,1])
3221
"""
degree_sequence.sort()
return sum(degree_sequence[i]*10**i for i in range(len(degree_sequence)))
def data_to_degseq(data, graph6=None):
"""
Takes the database integer data type (one digit per vertex
representing its degree, sorted high to low) and converts it to
degree sequence list. The graph6 identifier is required for all
graphs with no edges, so that the correct number of zeros will be
returned.
EXAMPLE::
sage: from sage.graphs.graph_database import data_to_degseq
sage: data_to_degseq(3221)
[1, 2, 2, 3]
sage: data_to_degseq(0,'D??')
[0, 0, 0, 0, 0]
"""
degseq = Integer(data).digits(10)
if not degseq:
from sage.graphs.generic_graph_pyx import N_inverse
return N_inverse(str(graph6))[0]*[0]
else:
return degseq
def graph6_to_plot(graph6):
"""
Constructs a graph from a graph6 string and returns a Graphics
object with arguments preset for show function.
EXAMPLE::
sage: from sage.graphs.graph_database import graph6_to_plot
sage: type(graph6_to_plot('D??'))
<class 'sage.plot.graphics.Graphics'>
"""
g = Graph(str(graph6))
return g.plot(layout='circular',vertex_size=30,vertex_labels=False,graph_border=False)
def subgraphs_to_query(subgraphs, db):
"""
Constructs and returns a GraphQuery object respecting the special
input required for the induced_subgraphs parameter. This input can
be an individual graph6 string (in which case it is evaluated
without the use of this method) or a list of strings. In the latter
case, the list should be of one of the following two formats: 1.
['one_of',String,...,String] Will search for graphs containing a
subgraph isomorphic to any of the graph6 strings in the list. 2.
['all_of',String,...,String] Will search for graphs containing a
subgraph isomorphic to each of the graph6 strings in the list.
This is a helper method called by the GraphQuery constructor to
handle this special format. This method should not be used on its
own because it doesn't set any display columns in the query string,
causing a failure to fetch the data when run.
EXAMPLE::
sage: from sage.graphs.graph_database import subgraphs_to_query
sage: gd = GraphDatabase()
sage: q = subgraphs_to_query(['all_of','A?','B?','C?'],gd)
sage: q.get_query_string()
'SELECT ,,,,, FROM misc WHERE ( ( misc.induced_subgraphs regexp ? ) AND (
misc.induced_subgraphs regexp ? ) ) AND ( misc.induced_subgraphs regexp ? )'
"""
q = GraphQuery(graph_db=db,induced_subgraphs=subgraphs[1])
if subgraphs[0] == 'all_of':
for i in range(len(subgraphs))[2:]:
q.intersect(GraphQuery(graph_db=db, induced_subgraphs=subgraphs[i]),in_place=True)
elif subgraphs[0] == 'one_of':
for i in range(len(subgraphs))[2:]:
q.union(GraphQuery(graph_db=db, induced_subgraphs=subgraphs[i]),in_place=True)
else:
raise KeyError, 'Unable to initiate query: Illegal input format for induced_subgraphs.'
return q
aut_grp = ['aut_grp_size',
'num_orbits',
'num_fixed_points',
'vertex_transitive',
'edge_transitive']
degrees = ['degree_sequence',
'min_degree',
'max_degree',
'average_degree',
'degrees_sd',
'regular']
misc = ['vertex_connectivity',
'edge_connectivity',
'num_components',
'girth',
'radius',
'diameter',
'clique_number',
'independence_number',
'num_cut_vertices',
'min_vertex_cover_size',
'num_spanning_trees',
'induced_subgraphs']
spectrum = ['spectrum',
'min_eigenvalue',
'max_eigenvalue',
'eigenvalues_sd',
'energy']
graph_data=['complement_graph6',
'eulerian',
'graph6',
'lovasz_number',
'num_cycles',
'num_edges',
'num_hamiltonian_cycles',
'num_vertices',
'perfect',
'planar']
valid_kwds = aut_grp + degrees + misc + spectrum + graph_data
def graph_db_info(tablename=None):
"""
Returns a dictionary of allowed table and column names.
INPUT:
- ``tablename`` - restricts the output to a single
table
EXAMPLE::
sage: graph_db_info().keys()
['graph_data', 'degrees', 'spectrum', 'misc', 'aut_grp']
::
sage: graph_db_info(tablename='graph_data')
['complement_graph6',
'eulerian',
'graph6',
'lovasz_number',
'num_cycles',
'num_edges',
'num_hamiltonian_cycles',
'num_vertices',
'perfect',
'planar']
"""
info = {'graph_data': graph_data,
'aut_grp': aut_grp,
'degrees': degrees,
'misc': misc,
'spectrum': spectrum}
if tablename is not None:
info = info[tablename]
return info
class GenericGraphQuery(SQLQuery):
def __init__(self, query_string, database=None, param_tuple=None):
"""
A query for a GraphDatabase.
INPUT:
- ``database`` - the GraphDatabase instance to query
(if None then a new instance is created)
- ``query_string`` - a string representing the SQL
query
- ``param_tuple`` - a tuple of strings - what to
replace question marks in query_string with (optional, but a good
idea)
.. note::
This query class is generally intended for developers and
more advanced users. It allows you to execute any query,
and so may be considered unsafe.
See GraphDatabase class docstrings or enter::
sage: G = GraphDatabase()
sage: G.get_skeleton()
{...
to see the underlying structure of the database. Also see
SQLQuery in sage.databases.database for more info and a
tutorial.
A piece of advice about '?' and param_tuple: It is generally
considered safer to query with a '?' in place of each value
parameter, and using a second argument (a tuple of strings) in a
call to the sqlite database. Successful use of the param_tuple
argument is exemplified::
sage: G = GraphDatabase()
sage: q = 'select graph_id,graph6,num_vertices,num_edges from graph_data where graph_id<=(?) and num_vertices=(?)'
sage: param = (22,5)
sage: Q = SQLQuery(G,q,param)
sage: Q.show()
graph_id graph6 num_vertices num_edges
--------------------------------------------------------------------------------
18 D?? 5 0
19 D?C 5 1
20 D?K 5 2
21 D@O 5 2
22 D?[ 5 3
"""
if database == None: database = GraphDatabase()
if not isinstance(database, GraphDatabase):
raise TypeError('%s is not a valid GraphDatabase'%database)
SQLQuery.__init__(self,database,query_string,param_tuple)
class GraphQuery(GenericGraphQuery):
def __init__(self, graph_db=None, query_dict=None, display_cols=None, **kwds):
"""
A query for an instance of GraphDatabase. This class nicely wraps
the SQLQuery class located in sage.databases.database.py to make
the query constraints intuitive and with as many pre-definitions as
possible. (i.e.: since it has to be a GraphDatabase, we already know
the table structure and types; and since it is immutable, we can
treat these as a guarantee).
.. note::
SQLQuery functions are available for GraphQuery. See
sage.dataabases.database.py for more details.
INPUT:
- ``graph_db`` - The GraphDatabase instance to apply
the query to. (If None, then a new instance is created).
- ``query_dict`` - A dictionary specifying the query
itself. Format is: 'table_name': 'tblname', 'display_cols':
['col1', 'col2'], 'expression':[col, operator, value] If not None,
query_dict will take precedence over all other arguments.
- ``display_cols`` - A list of column names (strings)
to display in the result when running or showing a query.
- ``kwds`` - The columns of the database are all
keywords. For a database table/column structure dictionary, call
graph_db_info. Keywords accept both single values and lists of
length 2. The list allows the user to specify an expression other
than equality. Valid expressions are strings, and for numeric
values (i.e. Reals and Integers) are: '=','','','=','='. String
values also accept 'regexp' as an expression argument. The only
keyword exception to this format is induced_subgraphs, which
accepts one of the following options: 1.
['one_of',String,...,String] Will search for graphs containing a
subgraph isomorphic to any of the graph6 strings in the list. 2.
['all_of',String,...,String] Will search for graphs containing a
subgraph isomorphic to each of the graph6 strings in the list.
EXAMPLES::
sage: Q = GraphQuery(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=['<=',5],min_degree=1)
sage: Q.number_of()
35
sage: Q.show()
Graph6 Num Vertices Degree Sequence
------------------------------------------------------------
A_ 2 [1, 1]
BW 3 [1, 1, 2]
CK 4 [1, 1, 1, 1]
CF 4 [1, 1, 1, 3]
CL 4 [1, 1, 2, 2]
CN 4 [1, 2, 2, 3]
D_K 5 [1, 1, 1, 1, 2]
D?{ 5 [1, 1, 1, 1, 4]
D@s 5 [1, 1, 1, 2, 3]
DBg 5 [1, 1, 2, 2, 2]
D`K 5 [1, 1, 2, 2, 2]
D@{ 5 [1, 1, 2, 2, 4]
DIk 5 [1, 2, 2, 2, 3]
DBk 5 [1, 1, 2, 3, 3]
DK[ 5 [1, 2, 2, 2, 3]
E@Q? 6 [1, 1, 1, 1, 1, 1]
E_?w 6 [1, 1, 1, 1, 1, 3]
E?N? 6 [1, 1, 1, 1, 2, 2]
E_Cg 6 [1, 1, 1, 1, 2, 2]
E?Bw 6 [1, 1, 1, 1, 1, 5]
E?Fg 6 [1, 1, 1, 1, 2, 4]
E@FG 6 [1, 1, 1, 2, 2, 3]
E?NG 6 [1, 1, 1, 1, 3, 3]
E@N? 6 [1, 1, 2, 2, 2, 2]
E@YO 6 [1, 1, 2, 2, 2, 2]
E@QW 6 [1, 1, 1, 2, 2, 3]
E_Cw 6 [1, 1, 1, 2, 2, 3]
E_Ko 6 [1, 1, 2, 2, 2, 2]
FK??W 7 [1, 1, 1, 1, 1, 1, 2]
F_?@w 7 [1, 1, 1, 1, 1, 1, 4]
F??^? 7 [1, 1, 1, 1, 1, 2, 3]
F_?Hg 7 [1, 1, 1, 1, 1, 2, 3]
F?LCG 7 [1, 1, 1, 1, 2, 2, 2]
F_?XO 7 [1, 1, 1, 1, 2, 2, 2]
FK?GW 7 [1, 1, 1, 1, 2, 2, 2]
"""
if graph_db == None: graph_db = GraphDatabase()
if query_dict is not None:
if query_dict['expression'][0] == 'degree_sequence':
query_dict['expression'][3] = degseq_to_data(query_dict['expression'][3])
elif query_dict['expression'][0] == 'induced_subgraphs':
query_dict['expression'][3] = subgraphs_to_data(query_dict['expression'][3])
SQLQuery.__init__(self, graph_db, query_dict)
else:
SQLQuery.__init__(self, graph_db)
master_join = {}
for key in kwds:
if not key in valid_kwds:
raise KeyError, '%s is not a valid key for this database.'%str(key)
qdict = {'display_cols': None}
if key in graph_data: qdict['table_name'] = 'graph_data'
elif key in aut_grp: qdict['table_name'] = 'aut_grp'
elif key in degrees: qdict['table_name'] = 'degrees'
elif key in misc: qdict['table_name'] = 'misc'
elif key in spectrum: qdict['table_name'] = 'spectrum'
if not isinstance(kwds[key],list):
if key == 'induced_subgraphs':
qdict['expression'] = [key, 'regexp', '.*%s.*'%(graph.Graph(kwds[key]).canonical_label()).graph6_string()]
else:
qdict['expression'] = [key, '=', kwds[key]]
elif key == 'degree_sequence':
qdict['expression'] = [key, '=', degseq_to_data(kwds[key])]
elif key != 'induced_subgraphs':
qdict['expression'] = [key] + kwds[key]
join_dict = {qdict['table_name']: ('graph_id', 'graph_id')}
if key == 'induced_subgraphs' and isinstance(kwds[key],list):
self.intersect(subgraphs_to_query(kwds[key], graph_db),
'graph_data', join_dict, in_place=True)
else:
self.intersect(SQLQuery(graph_db, qdict), 'graph_data', join_dict,in_place=True)
if qdict['table_name'] != 'graph_data':
master_join[qdict['table_name']] = ('graph_id', 'graph_id')
aut_grp_disp = ['aut_grp']
degrees_disp = ['degrees']
misc_disp = ['misc']
spectrum_disp = ['spectrum']
graph_data_disp = ['graph_data']
disp_tables = [aut_grp_disp, degrees_disp, misc_disp, spectrum_disp]
if display_cols is not None:
for col in display_cols:
if col in graph_data: graph_data_disp.append(col)
elif col in aut_grp: aut_grp_disp.append(col)
elif col in degrees: degrees_disp.append(col)
elif col in misc: misc_disp.append(col)
elif col in spectrum: spectrum_disp.append(col)
for tab in disp_tables:
if len(tab) > 1:
master_join[tab[0]] = ('graph_id', 'graph_id')
join_str = 'FROM graph_data '
for tab in master_join:
join_str += 'INNER JOIN %s ON graph_data.graph_id=%s.graph_id '%(tab, tab)
disp_str = 'SELECT graph_data.graph6, '
for col in graph_data_disp[1:]:
if col != 'graph6': disp_str += 'graph_data.%s, '%col
for col in aut_grp_disp[1:]: disp_str += 'aut_grp.%s, '%col
for col in degrees_disp[1:]: disp_str += 'degrees.%s, '%col
for col in misc_disp[1:]: disp_str += 'misc.%s, '%col
for col in spectrum_disp[1:]: disp_str += 'spectrum.%s, '%col
disp_str = disp_str.rstrip(', ') + ' '
self.__query_string__ = re.sub('SELECT.*WHERE ', disp_str + join_str + \
'WHERE ', self.__query_string__)
def query_iterator(self):
"""
Returns an iterator over the results list of the GraphQuery.
EXAMPLE::
sage: Q = GraphQuery(display_cols=['graph6'],num_vertices=7, diameter=5)
sage: for g in Q:
... print g.graph6_string()
F@?]O
F@OKg
F?`po
F?gqg
FIAHo
F@R@o
FA_pW
FGC{o
FEOhW
sage: Q = GraphQuery(display_cols=['graph6'],num_vertices=7, diameter=5)
sage: it = iter(Q)
sage: while True:
... try: print it.next().graph6_string()
... except StopIteration: break
F@?]O
F@OKg
F?`po
F?gqg
FIAHo
F@R@o
FA_pW
FGC{o
FEOhW
"""
return iter(self.get_graphs_list())
__iter__ = query_iterator
def show(self, max_field_size=20, with_picture=False):
"""
Displays the results of a query in table format.
INPUT:
- ``max_field_size`` - width of fields in command
prompt version
- ``with_picture`` - whether or not to display
results with a picture of the graph (available only in the
notebook)
EXAMPLES::
sage: G = GraphDatabase()
sage: Q = GraphQuery(G, display_cols=['graph6','num_vertices','aut_grp_size'], num_vertices=4, aut_grp_size=4)
sage: Q.show()
Graph6 Num Vertices Aut Grp Size
------------------------------------------------------------
C@ 4 4
C^ 4 4
::
sage: R = GraphQuery(G, display_cols=['graph6','num_vertices','degree_sequence'], num_vertices=4)
sage: R.show()
Graph6 Num Vertices Degree Sequence
------------------------------------------------------------
C? 4 [0, 0, 0, 0]
C@ 4 [0, 0, 1, 1]
CB 4 [0, 1, 1, 2]
CK 4 [1, 1, 1, 1]
CF 4 [1, 1, 1, 3]
CJ 4 [0, 2, 2, 2]
CL 4 [1, 1, 2, 2]
CN 4 [1, 2, 2, 3]
C] 4 [2, 2, 2, 2]
C^ 4 [2, 2, 3, 3]
C~ 4 [3, 3, 3, 3]
Show the pictures (in notebook mode only)::
sage: S = GraphQuery(G, display_cols=['graph6','aut_grp_size'], num_vertices=4)
sage: S.show(with_picture=True)
Traceback (most recent call last):
...
NotImplementedError: Cannot display plot on command line.
Note that pictures can be turned off::
sage: S.show(with_picture=False)
Graph6 Aut Grp Size
----------------------------------------
C? 24
C@ 4
CB 2
CK 8
CF 6
CJ 6
CL 2
CN 2
C] 8
C^ 4
C~ 24
Show your own query (note that the output is not reformatted for
generic queries)::
sage: (GenericGraphQuery('select degree_sequence from degrees where max_degree=2 and min_degree >= 1',G)).show()
degree_sequence
--------------------
211
222
2211
2222
21111
22211
22211
22222
221111
221111
222211
222211
222211
222222
222222
2111111
2221111
2221111
2221111
2222211
2222211
2222211
2222211
2222222
2222222
"""
relabel = {}
for col in valid_kwds:
relabel[col] = ' '.join([word.capitalize() for word in col.split('_')])
if re.search('SELECT .*degree_sequence.* FROM',self.__query_string__):
format_cols = {'degree_sequence': (lambda x,y: data_to_degseq(x,y))}
else: format_cols = {}
if with_picture:
SQLQuery.show(self, max_field_size=max_field_size, \
plot_cols={'graph6': (lambda x: graph6_to_plot(x))}, \
format_cols=format_cols, id_col='graph6', \
relabel_cols=relabel)
else:
SQLQuery.show(self, max_field_size=max_field_size, \
format_cols=format_cols, relabel_cols=relabel, \
id_col='graph6')
def get_graphs_list(self):
"""
Returns a list of Sage Graph objects that satisfy the query.
EXAMPLES::
sage: Q = GraphQuery(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=['<=',5],min_degree=1)
sage: L = Q.get_graphs_list()
sage: L[0]
Graph on 2 vertices
sage: len(L)
35
"""
from sage.graphs.graph_list import from_graph6
s = self.__query_string__
re.sub('SELECT.*FROM ', 'SELECT graph6 FROM ', s)
q = GenericGraphQuery(s, self.__database__, self.__param_tuple__)
graph6_list = q.query_results()
return [Graph(str(g[0])) for g in graph6_list]
def number_of(self):
"""
Returns the number of graphs in the database that satisfy the
query.
EXAMPLES::
sage: Q = GraphQuery(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=['<=',5],min_degree=1)
sage: Q.number_of()
35
"""
s = self.__query_string__
re.sub('SELECT.*FROM ', 'SELECT graph6 FROM ', s)
q = GenericGraphQuery(s, self.__database__, self.__param_tuple__)
return len(q.query_results())
class GraphDatabase(SQLDatabase):
def __init__(self):
"""
Graph Database
INFO:
This class interfaces with the sqlite database graphs.db. It is an
immutable database that inherits from SQLDatabase (see
sage.databases.database.py). The display functions and get_graphs_list
create their own queries, but it is also possible to query the
database by constructing either a SQLQuery.
The database contains all unlabeled graphs with 7 or fewer nodes.
This class will also interface with the optional database package
containing all unlabeled graphs with 8 or fewer nodes. The database
consists of five tables. For a full table and column structure,
call graph_db_info.
USE: The tables are associated by the unique primary key graph_id
(int).
To query this database, we create a GraphQuery. This can be done
directly with the query method or by initializing one of 1.
GenericGraphQuery - allows direct entry of a query string and tuple
of parameters. This is the route for more advanced users that are
familiar with SQL. 2. GraphQuery - is a wrapper of SQLQuery, a
general database/query wrapper of SQLite for new users.
REFERENCES:
- Data provided by Jason Grout (Brigham Young
University). [Online] Available:
http://math.byu.edu/~grout/graphs/
EXAMPLE::
sage: G = GraphDatabase()
sage: G.get_skeleton()
{u'aut_grp': {u'edge_transitive': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'vertex_transitive': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'aut_grp_size': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'graph_id': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'num_orbits': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'num_fixed_points': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'}},
u'degrees': {u'graph_id': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'degrees_sd': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'max_degree': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'regular': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'average_degree': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'degree_sequence': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'min_degree': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'}},
u'spectrum': {u'max_eigenvalue': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'energy': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'spectrum': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'TEXT'},
u'eigenvalues_sd': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'graph_id': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'min_eigenvalue': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'}},
u'misc': {u'diameter': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'vertex_connectivity': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'graph_id': {'index': False,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'num_components': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'min_vertex_cover_size': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'edge_connectivity': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'num_spanning_trees': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'induced_subgraphs': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'TEXT'},
u'radius': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'num_cut_vertices': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'clique_number': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'independence_number': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'girth': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'}},
u'graph_data': {u'perfect': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'planar': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'graph_id': {'index': True,
'unique': True,
'primary_key': False,
'sql': u'INTEGER'},
u'complement_graph6': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'TEXT'},
u'num_edges': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'num_cycles': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'graph6': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'TEXT'},
u'num_hamiltonian_cycles': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'},
u'lovasz_number': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'REAL'},
u'eulerian': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'BOOLEAN'},
u'num_vertices': {'index': True,
'unique': False,
'primary_key': False,
'sql': u'INTEGER'}}}
"""
SQLDatabase.__init__(self,dblocation)
def _gen_interact_func(self, display, **kwds):
"""
Generates and returns a function to interact with GraphQuery
parameters and results. This is a helper method for the
interactive_query method and should not be called directly.
EXAMPLE::
sage: D = GraphDatabase()
sage: D.interactive_query(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=['<=',5],max_degree=3)
<html>...</html>
::
sage: G = GraphDatabase()
sage: f = G._gen_interact_func(display=['graph6'], num_vertices=3)
sage: type(f)
<type 'function'>
sage: interact(f)
<html>...
"""
from sage.server.notebook.interact import input_grid
arg=['%s=%s'%(word,kwds[word]) for word in kwds]
boxes=["%s=input_grid(1,2,['=',%s])"%(word,kwds[word]) for word in kwds]
params = ['%s=%s[0]'%tuple(2*[arg[i].split('=')[0]]) for i in range(len(arg))]
s = 'def _(%s):'%','.join(boxes)
t = """
print '<html><h2>Query Results:</h2></html>'
GraphQuery(display_cols=%s,%s).show(with_picture=True)
"""%tuple([display,','.join(params)])
s += '\t'+'\n\t'.join(t.split('\n'))+'\n'
exec(s)
return _
def query(self, query_dict=None, display_cols=None, **kwds):
"""
Creates a GraphQuery on this database. For full class details, type
GraphQuery? and press shift+enter.
EXAMPLE::
sage: D = GraphDatabase()
sage: q = D.query(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=['<=',5])
sage: q.show()
Graph6 Num Vertices Degree Sequence
------------------------------------------------------------
@ 1 [0]
A? 2 [0, 0]
A_ 2 [1, 1]
B? 3 [0, 0, 0]
BG 3 [0, 1, 1]
BW 3 [1, 1, 2]
Bw 3 [2, 2, 2]
C? 4 [0, 0, 0, 0]
C@ 4 [0, 0, 1, 1]
CB 4 [0, 1, 1, 2]
CK 4 [1, 1, 1, 1]
CF 4 [1, 1, 1, 3]
CJ 4 [0, 2, 2, 2]
CL 4 [1, 1, 2, 2]
CN 4 [1, 2, 2, 3]
C] 4 [2, 2, 2, 2]
C^ 4 [2, 2, 3, 3]
D?? 5 [0, 0, 0, 0, 0]
D?C 5 [0, 0, 0, 1, 1]
D?K 5 [0, 0, 1, 1, 2]
D@O 5 [0, 1, 1, 1, 1]
D?[ 5 [0, 1, 1, 1, 3]
D@K 5 [0, 0, 2, 2, 2]
D_K 5 [1, 1, 1, 1, 2]
D@S 5 [0, 1, 1, 2, 2]
D?{ 5 [1, 1, 1, 1, 4]
D@[ 5 [0, 1, 2, 2, 3]
D@s 5 [1, 1, 1, 2, 3]
DBg 5 [1, 1, 2, 2, 2]
DBW 5 [0, 2, 2, 2, 2]
D`K 5 [1, 1, 2, 2, 2]
D@{ 5 [1, 1, 2, 2, 4]
DB[ 5 [0, 2, 2, 3, 3]
DIk 5 [1, 2, 2, 2, 3]
DBk 5 [1, 1, 2, 3, 3]
DK[ 5 [1, 2, 2, 2, 3]
DLo 5 [2, 2, 2, 2, 2]
E??? 6 [0, 0, 0, 0, 0, 0]
E??G 6 [0, 0, 0, 0, 1, 1]
E??W 6 [0, 0, 0, 1, 1, 2]
E?C_ 6 [0, 0, 1, 1, 1, 1]
E??w 6 [0, 0, 1, 1, 1, 3]
E?CW 6 [0, 0, 0, 2, 2, 2]
EG?W 6 [0, 1, 1, 1, 1, 2]
E?Cg 6 [0, 0, 1, 1, 2, 2]
E@Q? 6 [1, 1, 1, 1, 1, 1]
E?@w 6 [0, 1, 1, 1, 1, 4]
E?Cw 6 [0, 0, 1, 2, 2, 3]
E?Dg 6 [0, 1, 1, 1, 2, 3]
E_?w 6 [1, 1, 1, 1, 1, 3]
E?LO 6 [0, 1, 1, 2, 2, 2]
E?N? 6 [1, 1, 1, 1, 2, 2]
E?Ko 6 [0, 0, 2, 2, 2, 2]
EGCW 6 [0, 1, 1, 2, 2, 2]
E_Cg 6 [1, 1, 1, 1, 2, 2]
E?Bw 6 [1, 1, 1, 1, 1, 5]
E?Dw 6 [0, 1, 1, 2, 2, 4]
E?Fg 6 [1, 1, 1, 1, 2, 4]
E?Kw 6 [0, 0, 2, 2, 3, 3]
E@HW 6 [0, 1, 2, 2, 2, 3]
E@FG 6 [1, 1, 1, 2, 2, 3]
E?LW 6 [0, 1, 1, 2, 3, 3]
E?NG 6 [1, 1, 1, 1, 3, 3]
E@N? 6 [1, 1, 2, 2, 2, 2]
E@YO 6 [1, 1, 2, 2, 2, 2]
E@QW 6 [1, 1, 1, 2, 2, 3]
E@Ow 6 [0, 1, 2, 2, 2, 3]
E_Cw 6 [1, 1, 1, 2, 2, 3]
E@T_ 6 [0, 2, 2, 2, 2, 2]
E_Ko 6 [1, 1, 2, 2, 2, 2]
F???? 7 [0, 0, 0, 0, 0, 0, 0]
F???G 7 [0, 0, 0, 0, 0, 1, 1]
F???W 7 [0, 0, 0, 0, 1, 1, 2]
F??G_ 7 [0, 0, 0, 1, 1, 1, 1]
F???w 7 [0, 0, 0, 1, 1, 1, 3]
F??GW 7 [0, 0, 0, 0, 2, 2, 2]
F@??W 7 [0, 0, 1, 1, 1, 1, 2]
F??Gg 7 [0, 0, 0, 1, 1, 2, 2]
F?Ca? 7 [0, 1, 1, 1, 1, 1, 1]
F??@w 7 [0, 0, 1, 1, 1, 1, 4]
F??Gw 7 [0, 0, 0, 1, 2, 2, 3]
F??Hg 7 [0, 0, 1, 1, 1, 2, 3]
FG??w 7 [0, 1, 1, 1, 1, 1, 3]
F??XO 7 [0, 0, 1, 1, 2, 2, 2]
F??Z? 7 [0, 1, 1, 1, 1, 2, 2]
F??Wo 7 [0, 0, 0, 2, 2, 2, 2]
F@?GW 7 [0, 0, 1, 1, 2, 2, 2]
FK??W 7 [1, 1, 1, 1, 1, 1, 2]
FG?Gg 7 [0, 1, 1, 1, 1, 2, 2]
F??Bw 7 [0, 1, 1, 1, 1, 1, 5]
F??Hw 7 [0, 0, 1, 1, 2, 2, 4]
F??Jg 7 [0, 1, 1, 1, 1, 2, 4]
F_?@w 7 [1, 1, 1, 1, 1, 1, 4]
F??Ww 7 [0, 0, 0, 2, 2, 3, 3]
F?CPW 7 [0, 0, 1, 2, 2, 2, 3]
F?CJG 7 [0, 1, 1, 1, 2, 2, 3]
F??^? 7 [1, 1, 1, 1, 1, 2, 3]
F??XW 7 [0, 0, 1, 1, 2, 3, 3]
F??ZG 7 [0, 1, 1, 1, 1, 3, 3]
F?CZ? 7 [0, 1, 1, 2, 2, 2, 2]
F_?Hg 7 [1, 1, 1, 1, 1, 2, 3]
F?CqO 7 [0, 1, 1, 2, 2, 2, 2]
F?CaW 7 [0, 1, 1, 1, 2, 2, 3]
F?LCG 7 [1, 1, 1, 1, 2, 2, 2]
F?C_w 7 [0, 0, 1, 2, 2, 2, 3]
FG?Gw 7 [0, 1, 1, 1, 2, 2, 3]
F?Ch_ 7 [0, 0, 2, 2, 2, 2, 2]
FG?Wo 7 [0, 1, 1, 2, 2, 2, 2]
F_?XO 7 [1, 1, 1, 1, 2, 2, 2]
FK?GW 7 [1, 1, 1, 1, 2, 2, 2]
"""
return GraphQuery(self, query_dict, display_cols, **kwds)
def interactive_query(self, display_cols, **kwds):
"""
TODO: This function could use improvement. Add full options of
typical GraphQuery (i.e.: have it accept list input); and update
options in interact to make it less annoying to put in operators.
Generates an interact shell (in the notebook only) that allows the
user to manipulate query parameters and see the updated results.
EXAMPLE::
sage: D = GraphDatabase()
sage: D.interactive_query(display_cols=['graph6','num_vertices','degree_sequence'],num_edges=5,max_degree=3)
<html>...</html>
"""
from sage.server.notebook.interact import interact
print '<html><h1>Interactive Graph Query</h1></html>'
f = self._gen_interact_func(display=display_cols,**kwds)
interact(f)
