Graph database

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.sql_db).

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_db_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.sql_db.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:

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:

  • query_string – a string representing the SQL query
  • database – (default: None); the GraphDatabase instance to query (if None then a new instance is created)
  • param_tuple – a tuple of strings (default: None); 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.

EXAMPLES:

See GraphDatabase class docstrings or enter:

sage: G = GraphDatabase()
sage: G.get_skeleton()
{...

to see the underlying structure of the database. Also see sage.databases.sql_db.SQLQuery in sage.databases.sql_db 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
class sage.graphs.graph_database.GraphDatabase

Bases: sage.databases.sql_db.SQLDatabase

Graph Database

This class interfaces with the sqlite database graphs.db. It is an immutable database that inherits from SQLDatabase (see sage.databases.sql_db). 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().

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:

  • 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
  • GraphQuery – a wrapper of SQLQuery, a general database/query wrapper of SQLite for new users

REFERENCES:

EXAMPLES:

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}}}
interactive_query(display_cols, **kwds)

Generate an interact shell to query the database.

This method generates an interact shell (in the notebook only) that allows the user to manipulate query parameters and see the updated results.

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.

EXAMPLES:

sage: D = GraphDatabase()
sage: D.interactive_query(display_cols=['graph6', 'num_vertices', 'degree_sequence'], num_edges=5, max_degree=3)  # py2
<html>...</html>

Warning

Above doctest is known to fail with Python 3 due to sagenb. See trac ticket #27435 for more details.

query(query_dict=None, display_cols=None, **kwds)

Create a GraphQuery on this database.

For full class details, type GraphQuery? and press shift+enter.

EXAMPLES:

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]
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 sage.databases.sql_db.SQLQuery class located in sage.databases.sql_db 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

sage.databases.sql_db.SQLQuery functions are available for GraphQuery. See sage.databases.sql_db for more details.

INPUT:

  • graph_dbGraphDatabase (default: None); instance to apply the query to (If None, then a new instance is created)
  • query_dict – dict (default: None); 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 – list of strings (default: None); 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:
    • ['one_of', String, ..., String] – will search for graphs containing a subgraph isomorphic to any of the graph6 strings in the list
    • ['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]
get_graphs_list()

Return 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
number_of()

Return 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
query_iterator()

Return an iterator over the results list of the GraphQuery.

EXAMPLES:

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
show(max_field_size=20, with_picture=False)

Display the results of a query in table format.

INPUT:

  • max_field_size – integer (default: 20); width of fields in command prompt version
  • with_picture – boolean (default: False); 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
sage.graphs.graph_database.data_to_degseq(data, graph6=None)

Convert a database integer data type to a degree sequence list.

INPUT:

  • data – integer data type (one digit per vertex representing its degree, sorted high to low) to be converted to a degree sequence list
  • graph6 – string (default: None); the graph6 identifier is required for all graphs with no edges, so that the correct number of zeros is returned.

EXAMPLES:

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]
sage.graphs.graph_database.degseq_to_data(degree_sequence)

Convert a degree sequence list to a sorted (max-min) integer data type.

The input degree sequence list (of Integers) is converted to a sorted (max-min) integer data type, as used for faster access in the underlying database.

INPUT:

  • degree_sequence – list of integers; input degree sequence list

EXAMPLES:

sage: from sage.graphs.graph_database import degseq_to_data
sage: degseq_to_data([2,2,3,1])
3221
sage.graphs.graph_database.graph6_to_plot(graph6)

Return a Graphics object from a graph6 string.

This method constructs a graph from a graph6 string and returns a sage.plot.graphics.Graphics object with arguments preset for the sage.plot.graphics.Graphics.show() method.

INPUT:

  • graph6 – a graph6 string

EXAMPLES:

sage: from sage.graphs.graph_database import graph6_to_plot
sage: type(graph6_to_plot('D??'))
<class 'sage.plot.graphics.Graphics'>
sage.graphs.graph_database.graph_db_info(tablename=None)

Return a dictionary of allowed table and column names.

INPUT:

  • tablename – restricts the output to a single table

EXAMPLES:

sage: sorted(graph_db_info())
['aut_grp', 'degrees', 'graph_data', 'misc', 'spectrum']
sage: graph_db_info(tablename='graph_data')
['complement_graph6',
 'eulerian',
 'graph6',
 'lovasz_number',
 'num_cycles',
 'num_edges',
 'num_hamiltonian_cycles',
 'num_vertices',
 'perfect',
 'planar']
sage.graphs.graph_database.subgraphs_to_query(subgraphs, db)

Return a GraphQuery object required for the induced_subgraphs parameter.

This method constructs and returns a GraphQuery object respecting the special input required for the induced_subgraphs parameter.

INPUT:

  • subgraphs – list of strings; the list should be of one of the following two formats:
    • ['one_of', String, ..., String] – will search for graphs containing a subgraph isomorphic to any of the graph6 strings in the list
    • ['all_of', String, ..., String] – will search for graphs containing a subgraph isomorphic to each of the graph6 strings in the list
  • db – a GraphDatabase

Note

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.

EXAMPLES:

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 ? )'