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Source code for networkx.generators.small

# -*- coding: utf-8 -*-
Various small and named graphs, together with some compact generators.

__author__ ="""Aric Hagberg (hagberg@lanl.gov)\nPieter Swart (swart@lanl.gov)"""
#    Copyright (C) 2004-2008 by 
#    Aric Hagberg <hagberg@lanl.gov>
#    Dan Schult <dschult@colgate.edu>
#    Pieter Swart <swart@lanl.gov>
#    All rights reserved.
#    BSD license.

__all__ = ['make_small_graph',

import networkx as nx
from networkx.generators.classic import empty_graph, cycle_graph, path_graph, complete_graph
from networkx.exception import NetworkXError

#   Tools for creating small graphs
def make_small_undirected_graph(graph_description, create_using=None):
    Return a small undirected graph described by graph_description.

    See make_small_graph.
    if create_using is not None and create_using.is_directed():
        raise NetworkXError("Directed Graph not supported")
    return make_small_graph(graph_description, create_using)

[docs]def make_small_graph(graph_description, create_using=None): """ Return the small graph described by graph_description. graph_description is a list of the form [ltype,name,n,xlist] Here ltype is one of "adjacencylist" or "edgelist", name is the name of the graph and n the number of nodes. This constructs a graph of n nodes with integer labels 0,..,n-1. If ltype="adjacencylist" then xlist is an adjacency list with exactly n entries, in with the j'th entry (which can be empty) specifies the nodes connected to vertex j. e.g. the "square" graph C_4 can be obtained by >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[1,3],[2,4],[1,3]]]) or, since we do not need to add edges twice, >>> G=nx.make_small_graph(["adjacencylist","C_4",4,[[2,4],[3],[4],[]]]) If ltype="edgelist" then xlist is an edge list written as [[v1,w2],[v2,w2],...,[vk,wk]], where vj and wj integers in the range 1,..,n e.g. the "square" graph C_4 can be obtained by >>> G=nx.make_small_graph(["edgelist","C_4",4,[[1,2],[3,4],[2,3],[4,1]]]) Use the create_using argument to choose the graph class/type. """ ltype=graph_description[0] name=graph_description[1] n=graph_description[2] G=empty_graph(n, create_using) nodes=G.nodes() if ltype=="adjacencylist": adjlist=graph_description[3] if len(adjlist) != n: raise NetworkXError("invalid graph_description") G.add_edges_from([(u-1,v) for v in nodes for u in adjlist[v]]) elif ltype=="edgelist": edgelist=graph_description[3] for e in edgelist: v1=e[0]-1 v2=e[1]-1 if v1<0 or v1>n-1 or v2<0 or v2>n-1: raise NetworkXError("invalid graph_description") else: G.add_edge(v1,v2) G.name=name return G
[docs]def LCF_graph(n,shift_list,repeats,create_using=None): """ Return the cubic graph specified in LCF notation. LCF notation (LCF=Lederberg-Coxeter-Fruchte) is a compressed notation used in the generation of various cubic Hamiltonian graphs of high symmetry. See, for example, dodecahedral_graph, desargues_graph, heawood_graph and pappus_graph below. n (number of nodes) The starting graph is the n-cycle with nodes 0,...,n-1. (The null graph is returned if n < 0.) shift_list = [s1,s2,..,sk], a list of integer shifts mod n, repeats integer specifying the number of times that shifts in shift_list are successively applied to each v_current in the n-cycle to generate an edge between v_current and v_current+shift mod n. For v1 cycling through the n-cycle a total of k*repeats with shift cycling through shiftlist repeats times connect v1 with v1+shift mod n The utility graph K_{3,3} >>> G=nx.LCF_graph(6,[3,-3],3) The Heawood graph >>> G=nx.LCF_graph(14,[5,-5],7) See http://mathworld.wolfram.com/LCFNotation.html for a description and references. """ if create_using is not None and create_using.is_directed(): raise NetworkXError("Directed Graph not supported") if n <= 0: return empty_graph(0, create_using) # start with the n-cycle G=cycle_graph(n, create_using) G.name="LCF_graph" nodes=G.nodes() n_extra_edges=repeats*len(shift_list) # edges are added n_extra_edges times # (not all of these need be new) if n_extra_edges < 1: return G for i in range(n_extra_edges): shift=shift_list[i%len(shift_list)] #cycle through shift_list v1=nodes[i%n] # cycle repeatedly through nodes v2=nodes[(i + shift)%n] G.add_edge(v1, v2) return G #------------------------------------------------------------------------------- # Various small and named graphs #-------------------------------------------------------------------------------
[docs]def bull_graph(create_using=None): """Return the Bull graph. """ description=[ "adjacencylist", "Bull Graph", 5, [[2,3],[1,3,4],[1,2,5],[2],[3]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def chvatal_graph(create_using=None): """Return the Chvátal graph.""" description=[ "adjacencylist", "Chvatal Graph", 12, [[2,5,7,10],[3,6,8],[4,7,9],[5,8,10], [6,9],[11,12],[11,12],[9,12], [11],[11,12],[],[]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def cubical_graph(create_using=None): """Return the 3-regular Platonic Cubical graph.""" description=[ "adjacencylist", "Platonic Cubical Graph", 8, [[2,4,5],[1,3,8],[2,4,7],[1,3,6], [1,6,8],[4,5,7],[3,6,8],[2,5,7]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def desargues_graph(create_using=None): """ Return the Desargues graph.""" G=LCF_graph(20, [5,-5,9,-9], 5, create_using) G.name="Desargues Graph" return G
[docs]def diamond_graph(create_using=None): """Return the Diamond graph. """ description=[ "adjacencylist", "Diamond Graph", 4, [[2,3],[1,3,4],[1,2,4],[2,3]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def dodecahedral_graph(create_using=None): """ Return the Platonic Dodecahedral graph. """ G=LCF_graph(20, [10,7,4,-4,-7,10,-4,7,-7,4], 2, create_using) G.name="Dodecahedral Graph" return G
[docs]def frucht_graph(create_using=None): """Return the Frucht Graph. The Frucht Graph is the smallest cubical graph whose automorphism group consists only of the identity element. """ G=cycle_graph(7, create_using) G.add_edges_from([[0,7],[1,7],[2,8],[3,9],[4,9],[5,10],[6,10], [7,11],[8,11],[8,9],[10,11]]) G.name="Frucht Graph" return G
[docs]def heawood_graph(create_using=None): """ Return the Heawood graph, a (3,6) cage. """ G=LCF_graph(14, [5,-5], 7, create_using) G.name="Heawood Graph" return G
[docs]def house_graph(create_using=None): """Return the House graph (square with triangle on top).""" description=[ "adjacencylist", "House Graph", 5, [[2,3],[1,4],[1,4,5],[2,3,5],[3,4]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def house_x_graph(create_using=None): """Return the House graph with a cross inside the house square.""" description=[ "adjacencylist", "House-with-X-inside Graph", 5, [[2,3,4],[1,3,4],[1,2,4,5],[1,2,3,5],[3,4]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def icosahedral_graph(create_using=None): """Return the Platonic Icosahedral graph.""" description=[ "adjacencylist", "Platonic Icosahedral Graph", 12, [[2,6,8,9,12],[3,6,7,9],[4,7,9,10],[5,7,10,11], [6,7,11,12],[7,12],[],[9,10,11,12], [10],[11],[12],[]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def krackhardt_kite_graph(create_using=None): """ Return the Krackhardt Kite Social Network. A 10 actor social network introduced by David Krackhardt to illustrate: degree, betweenness, centrality, closeness, etc. The traditional labeling is: Andre=1, Beverley=2, Carol=3, Diane=4, Ed=5, Fernando=6, Garth=7, Heather=8, Ike=9, Jane=10. """ description=[ "adjacencylist", "Krackhardt Kite Social Network", 10, [[2,3,4,6],[1,4,5,7],[1,4,6],[1,2,3,5,6,7],[2,4,7], [1,3,4,7,8],[2,4,5,6,8],[6,7,9],[8,10],[9]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def moebius_kantor_graph(create_using=None): """Return the Moebius-Kantor graph.""" G=LCF_graph(16, [5,-5], 8, create_using) G.name="Moebius-Kantor Graph" return G
[docs]def octahedral_graph(create_using=None): """Return the Platonic Octahedral graph.""" description=[ "adjacencylist", "Platonic Octahedral Graph", 6, [[2,3,4,5],[3,4,6],[5,6],[5,6],[6],[]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def pappus_graph(): """ Return the Pappus graph.""" G=LCF_graph(18,[5,7,-7,7,-7,-5],3) G.name="Pappus Graph" return G
[docs]def petersen_graph(create_using=None): """Return the Petersen graph.""" description=[ "adjacencylist", "Petersen Graph", 10, [[2,5,6],[1,3,7],[2,4,8],[3,5,9],[4,1,10],[1,8,9],[2,9,10], [3,6,10],[4,6,7],[5,7,8]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def sedgewick_maze_graph(create_using=None): """ Return a small maze with a cycle. This is the maze used in Sedgewick,3rd Edition, Part 5, Graph Algorithms, Chapter 18, e.g. Figure 18.2 and following. Nodes are numbered 0,..,7 """ G=empty_graph(0, create_using) G.add_nodes_from(range(8)) G.add_edges_from([[0,2],[0,7],[0,5]]) G.add_edges_from([[1,7],[2,6]]) G.add_edges_from([[3,4],[3,5]]) G.add_edges_from([[4,5],[4,7],[4,6]]) G.name="Sedgewick Maze" return G
[docs]def tetrahedral_graph(create_using=None): """ Return the 3-regular Platonic Tetrahedral graph.""" G=complete_graph(4, create_using) G.name="Platonic Tetrahedral graph" return G
[docs]def truncated_cube_graph(create_using=None): """Return the skeleton of the truncated cube.""" description=[ "adjacencylist", "Truncated Cube Graph", 24, [[2,3,5],[12,15],[4,5],[7,9], [6],[17,19],[8,9],[11,13], [10],[18,21],[12,13],[15], [14],[22,23],[16],[20,24], [18,19],[21],[20],[24], [22],[23],[24],[]] ] G=make_small_undirected_graph(description, create_using) return G
[docs]def truncated_tetrahedron_graph(create_using=None): """Return the skeleton of the truncated Platonic tetrahedron.""" G=path_graph(12, create_using) # G.add_edges_from([(1,3),(1,10),(2,7),(4,12),(5,12),(6,8),(9,11)]) G.add_edges_from([(0,2),(0,9),(1,6),(3,11),(4,11),(5,7),(8,10)]) G.name="Truncated Tetrahedron Graph" return G
[docs]def tutte_graph(create_using=None): """Return the Tutte graph.""" description=[ "adjacencylist", "Tutte's Graph", 46, [[2,3,4],[5,27],[11,12],[19,20],[6,34], [7,30],[8,28],[9,15],[10,39],[11,38], [40],[13,40],[14,36],[15,16],[35], [17,23],[18,45],[19,44],[46],[21,46], [22,42],[23,24],[41],[25,28],[26,33], [27,32],[34],[29],[30,33],[31], [32,34],[33],[],[],[36,39], [37],[38,40],[39],[],[], [42,45],[43],[44,46],[45],[],[]] ] G=make_small_undirected_graph(description, create_using) return G