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://artsci.drake.edu/grout/graphs/
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class
sage.graphs.graph_database.
GenericGraphQuery
(query_string, database=None, param_tuple=None)¶ Bases:
sage.databases.sql_db.SQLQuery
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 queryparam_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
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class
sage.graphs.graph_database.
GraphDatabase
¶ Bases:
sage.databases.sql_db.SQLDatabase
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://artsci.drake.edu/grout/graphs/
EXAMPLE:
sage: G = GraphDatabase() sage: G.get_skeleton() {u'aut_grp': {u'aut_grp_size': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'edge_transitive': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}, u'graph_id': {'index': False, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_fixed_points': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_orbits': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'vertex_transitive': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}}, u'degrees': {u'average_degree': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'degree_sequence': {'index': False, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'degrees_sd': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'graph_id': {'index': False, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'max_degree': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'min_degree': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'regular': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}}, u'graph_data': {u'complement_graph6': {'index': True, 'primary_key': False, 'sql': u'TEXT', 'unique': False}, u'eulerian': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}, u'graph6': {'index': True, 'primary_key': False, 'sql': u'TEXT', 'unique': False}, u'graph_id': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': True}, u'lovasz_number': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'num_cycles': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_edges': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_hamiltonian_cycles': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_vertices': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'perfect': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}, u'planar': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}}, u'misc': {u'clique_number': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'diameter': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'edge_connectivity': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}, u'girth': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'graph_id': {'index': False, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'independence_number': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'induced_subgraphs': {'index': True, 'primary_key': False, 'sql': u'TEXT', 'unique': False}, u'min_vertex_cover_size': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_components': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_cut_vertices': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'num_spanning_trees': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'radius': {'index': True, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'vertex_connectivity': {'index': True, 'primary_key': False, 'sql': u'BOOLEAN', 'unique': False}}, u'spectrum': {u'eigenvalues_sd': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'energy': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'graph_id': {'index': False, 'primary_key': False, 'sql': u'INTEGER', 'unique': False}, u'max_eigenvalue': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'min_eigenvalue': {'index': True, 'primary_key': False, 'sql': u'REAL', 'unique': False}, u'spectrum': {'index': False, 'primary_key': False, 'sql': u'TEXT', 'unique': False}}}
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interactive_query
(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>
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query
(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] CF 4 [1, 1, 1, 3] CJ 4 [0, 2, 2, 2] CK 4 [1, 1, 1, 1] 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?[ 5 [0, 1, 1, 1, 3] D?{ 5 [1, 1, 1, 1, 4] D@K 5 [0, 0, 2, 2, 2] D@O 5 [0, 1, 1, 1, 1] D@S 5 [0, 1, 1, 2, 2] D@[ 5 [0, 1, 2, 2, 3] D@s 5 [1, 1, 1, 2, 3] D@{ 5 [1, 1, 2, 2, 4] DBW 5 [0, 2, 2, 2, 2] DB[ 5 [0, 2, 2, 3, 3] DBg 5 [1, 1, 2, 2, 2] DBk 5 [1, 1, 2, 3, 3] DIk 5 [1, 2, 2, 2, 3] DK[ 5 [1, 2, 2, 2, 3] DLo 5 [2, 2, 2, 2, 2] D_K 5 [1, 1, 1, 1, 2] D`K 5 [1, 1, 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??w 6 [0, 0, 1, 1, 1, 3] E?@w 6 [0, 1, 1, 1, 1, 4] E?Bw 6 [1, 1, 1, 1, 1, 5] E?CW 6 [0, 0, 0, 2, 2, 2] E?C_ 6 [0, 0, 1, 1, 1, 1] E?Cg 6 [0, 0, 1, 1, 2, 2] E?Cw 6 [0, 0, 1, 2, 2, 3] E?Dg 6 [0, 1, 1, 1, 2, 3] E?Dw 6 [0, 1, 1, 2, 2, 4] E?Fg 6 [1, 1, 1, 1, 2, 4] E?Ko 6 [0, 0, 2, 2, 2, 2] E?Kw 6 [0, 0, 2, 2, 3, 3] E?LO 6 [0, 1, 1, 2, 2, 2] E?LW 6 [0, 1, 1, 2, 3, 3] E?N? 6 [1, 1, 1, 1, 2, 2] E?NG 6 [1, 1, 1, 1, 3, 3] E@FG 6 [1, 1, 1, 2, 2, 3] E@HW 6 [0, 1, 2, 2, 2, 3] E@N? 6 [1, 1, 2, 2, 2, 2] E@Ow 6 [0, 1, 2, 2, 2, 3] E@Q? 6 [1, 1, 1, 1, 1, 1] E@QW 6 [1, 1, 1, 2, 2, 3] E@T_ 6 [0, 2, 2, 2, 2, 2] E@YO 6 [1, 1, 2, 2, 2, 2] EG?W 6 [0, 1, 1, 1, 1, 2] EGCW 6 [0, 1, 1, 2, 2, 2] E_?w 6 [1, 1, 1, 1, 1, 3] E_Cg 6 [1, 1, 1, 1, 2, 2] E_Cw 6 [1, 1, 1, 2, 2, 3] 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???w 7 [0, 0, 0, 1, 1, 1, 3] F??@w 7 [0, 0, 1, 1, 1, 1, 4] F??Bw 7 [0, 1, 1, 1, 1, 1, 5] F??GW 7 [0, 0, 0, 0, 2, 2, 2] F??G_ 7 [0, 0, 0, 1, 1, 1, 1] F??Gg 7 [0, 0, 0, 1, 1, 2, 2] F??Gw 7 [0, 0, 0, 1, 2, 2, 3] F??Hg 7 [0, 0, 1, 1, 1, 2, 3] F??Hw 7 [0, 0, 1, 1, 2, 2, 4] F??Jg 7 [0, 1, 1, 1, 1, 2, 4] F??Wo 7 [0, 0, 0, 2, 2, 2, 2] F??Ww 7 [0, 0, 0, 2, 2, 3, 3] F??XO 7 [0, 0, 1, 1, 2, 2, 2] F??XW 7 [0, 0, 1, 1, 2, 3, 3] F??Z? 7 [0, 1, 1, 1, 1, 2, 2] F??ZG 7 [0, 1, 1, 1, 1, 3, 3] F??^? 7 [1, 1, 1, 1, 1, 2, 3] F?CJG 7 [0, 1, 1, 1, 2, 2, 3] F?CPW 7 [0, 0, 1, 2, 2, 2, 3] F?CZ? 7 [0, 1, 1, 2, 2, 2, 2] F?C_w 7 [0, 0, 1, 2, 2, 2, 3] F?Ca? 7 [0, 1, 1, 1, 1, 1, 1] F?CaW 7 [0, 1, 1, 1, 2, 2, 3] F?Ch_ 7 [0, 0, 2, 2, 2, 2, 2] F?CqO 7 [0, 1, 1, 2, 2, 2, 2] F?LCG 7 [1, 1, 1, 1, 2, 2, 2] F@??W 7 [0, 0, 1, 1, 1, 1, 2] F@?GW 7 [0, 0, 1, 1, 2, 2, 2] FG??w 7 [0, 1, 1, 1, 1, 1, 3] FG?Gg 7 [0, 1, 1, 1, 1, 2, 2] FG?Gw 7 [0, 1, 1, 1, 2, 2, 3] FG?Wo 7 [0, 1, 1, 2, 2, 2, 2] FK??W 7 [1, 1, 1, 1, 1, 1, 2] FK?GW 7 [1, 1, 1, 1, 2, 2, 2] F_?@w 7 [1, 1, 1, 1, 1, 1, 4] F_?Hg 7 [1, 1, 1, 1, 1, 2, 3] F_?XO 7 [1, 1, 1, 1, 2, 2, 2]
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class
sage.graphs.graph_database.
GraphQuery
(graph_db=None, query_dict=None, display_cols=None, **kwds)¶ Bases:
sage.graphs.graph_database.GenericGraphQuery
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] CF 4 [1, 1, 1, 3] CK 4 [1, 1, 1, 1] CL 4 [1, 1, 2, 2] CN 4 [1, 2, 2, 3] D?{ 5 [1, 1, 1, 1, 4] D@s 5 [1, 1, 1, 2, 3] D@{ 5 [1, 1, 2, 2, 4] DBg 5 [1, 1, 2, 2, 2] DBk 5 [1, 1, 2, 3, 3] DIk 5 [1, 2, 2, 2, 3] DK[ 5 [1, 2, 2, 2, 3] D_K 5 [1, 1, 1, 1, 2] D`K 5 [1, 1, 2, 2, 2] E?Bw 6 [1, 1, 1, 1, 1, 5] E?Fg 6 [1, 1, 1, 1, 2, 4] E?N? 6 [1, 1, 1, 1, 2, 2] E?NG 6 [1, 1, 1, 1, 3, 3] E@FG 6 [1, 1, 1, 2, 2, 3] E@N? 6 [1, 1, 2, 2, 2, 2] E@Q? 6 [1, 1, 1, 1, 1, 1] E@QW 6 [1, 1, 1, 2, 2, 3] E@YO 6 [1, 1, 2, 2, 2, 2] E_?w 6 [1, 1, 1, 1, 1, 3] E_Cg 6 [1, 1, 1, 1, 2, 2] E_Cw 6 [1, 1, 1, 2, 2, 3] E_Ko 6 [1, 1, 2, 2, 2, 2] F??^? 7 [1, 1, 1, 1, 1, 2, 3] F?LCG 7 [1, 1, 1, 1, 2, 2, 2] FK??W 7 [1, 1, 1, 1, 1, 1, 2] FK?GW 7 [1, 1, 1, 1, 2, 2, 2] F_?@w 7 [1, 1, 1, 1, 1, 1, 4] F_?Hg 7 [1, 1, 1, 1, 1, 2, 3] F_?XO 7 [1, 1, 1, 1, 2, 2, 2]
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get_graphs_list
()¶ 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
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number_of
()¶ 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
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query_iterator
()¶ 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?`po F?gqg F@?]O F@OKg F@R@o FA_pW FEOhW FGC{o FIAHo sage: Q = GraphQuery(display_cols=['graph6'],num_vertices=7, diameter=5) sage: it = iter(Q) sage: while True: ....: try: print(next(it).graph6_string()) ....: except StopIteration: break F?`po F?gqg F@?]O F@OKg F@R@o FA_pW FEOhW FGC{o FIAHo
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show
(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 versionwith_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] CF 4 [1, 1, 1, 3] CJ 4 [0, 2, 2, 2] CK 4 [1, 1, 1, 1] 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 CF 6 CJ 6 CK 8 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
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sage.graphs.graph_database.
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]
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sage.graphs.graph_database.
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
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sage.graphs.graph_database.
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'>
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sage.graphs.graph_database.
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']
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sage.graphs.graph_database.
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 ? )'