Shared2015-08-03-161507.sagewsOpen in CoCalc
Author: Szabolcs Tengely
Views : 34
def Arrangement1n(n): G=Graph() G.add_vertices([1..n]) Gedges=[] for i in [1..n]: for j in [i+1..n]: if (i+j).is_perfect_power(): Gedges.append([i,j]) G.add_edges(Gedges) G.show(layout='circular') print latex(G) if G.is_hamiltonian(): G.hamiltonian_cycle().show() return True else: G.add_vertex(0) for i in [1..n]: G.add_edges([[0,i]]) if G.is_hamiltonian(): G.hamiltonian_cycle().show() return True else: return False Arrangement1n(19)
\begin{tikzpicture} \definecolor{cv0}{rgb}{0.0,0.0,0.0} \definecolor{cfv0}{rgb}{1.0,1.0,1.0} \definecolor{clv0}{rgb}{0.0,0.0,0.0} \definecolor{cv1}{rgb}{0.0,0.0,0.0} \definecolor{cfv1}{rgb}{1.0,1.0,1.0} \definecolor{clv1}{rgb}{0.0,0.0,0.0} \definecolor{cv2}{rgb}{0.0,0.0,0.0} \definecolor{cfv2}{rgb}{1.0,1.0,1.0} \definecolor{clv2}{rgb}{0.0,0.0,0.0} \definecolor{cv3}{rgb}{0.0,0.0,0.0} \definecolor{cfv3}{rgb}{1.0,1.0,1.0} \definecolor{clv3}{rgb}{0.0,0.0,0.0} \definecolor{cv4}{rgb}{0.0,0.0,0.0} \definecolor{cfv4}{rgb}{1.0,1.0,1.0} \definecolor{clv4}{rgb}{0.0,0.0,0.0} \definecolor{cv5}{rgb}{0.0,0.0,0.0} \definecolor{cfv5}{rgb}{1.0,1.0,1.0} \definecolor{clv5}{rgb}{0.0,0.0,0.0} \definecolor{cv6}{rgb}{0.0,0.0,0.0} \definecolor{cfv6}{rgb}{1.0,1.0,1.0} \definecolor{clv6}{rgb}{0.0,0.0,0.0} \definecolor{cv7}{rgb}{0.0,0.0,0.0} \definecolor{cfv7}{rgb}{1.0,1.0,1.0} \definecolor{clv7}{rgb}{0.0,0.0,0.0} \definecolor{cv8}{rgb}{0.0,0.0,0.0} \definecolor{cfv8}{rgb}{1.0,1.0,1.0} \definecolor{clv8}{rgb}{0.0,0.0,0.0} \definecolor{cv9}{rgb}{0.0,0.0,0.0} \definecolor{cfv9}{rgb}{1.0,1.0,1.0} \definecolor{clv9}{rgb}{0.0,0.0,0.0} \definecolor{cv10}{rgb}{0.0,0.0,0.0} \definecolor{cfv10}{rgb}{1.0,1.0,1.0} \definecolor{clv10}{rgb}{0.0,0.0,0.0} \definecolor{cv11}{rgb}{0.0,0.0,0.0} \definecolor{cfv11}{rgb}{1.0,1.0,1.0} \definecolor{clv11}{rgb}{0.0,0.0,0.0} \definecolor{cv12}{rgb}{0.0,0.0,0.0} \definecolor{cfv12}{rgb}{1.0,1.0,1.0} \definecolor{clv12}{rgb}{0.0,0.0,0.0} \definecolor{cv13}{rgb}{0.0,0.0,0.0} \definecolor{cfv13}{rgb}{1.0,1.0,1.0} \definecolor{clv13}{rgb}{0.0,0.0,0.0} \definecolor{cv14}{rgb}{0.0,0.0,0.0} \definecolor{cfv14}{rgb}{1.0,1.0,1.0} \definecolor{clv14}{rgb}{0.0,0.0,0.0} \definecolor{cv15}{rgb}{0.0,0.0,0.0} \definecolor{cfv15}{rgb}{1.0,1.0,1.0} \definecolor{clv15}{rgb}{0.0,0.0,0.0} \definecolor{cv16}{rgb}{0.0,0.0,0.0} \definecolor{cfv16}{rgb}{1.0,1.0,1.0} \definecolor{clv16}{rgb}{0.0,0.0,0.0} \definecolor{cv17}{rgb}{0.0,0.0,0.0} \definecolor{cfv17}{rgb}{1.0,1.0,1.0} \definecolor{clv17}{rgb}{0.0,0.0,0.0} \definecolor{cv18}{rgb}{0.0,0.0,0.0} \definecolor{cfv18}{rgb}{1.0,1.0,1.0} \definecolor{clv18}{rgb}{0.0,0.0,0.0} \definecolor{cv9v16}{rgb}{0.0,0.0,0.0} \definecolor{cv5v9}{rgb}{0.0,0.0,0.0} \definecolor{cv9v14}{rgb}{0.0,0.0,0.0} \definecolor{cv0v2}{rgb}{0.0,0.0,0.0} \definecolor{cv0v6}{rgb}{0.0,0.0,0.0} \definecolor{cv0v7}{rgb}{0.0,0.0,0.0} \definecolor{cv0v14}{rgb}{0.0,0.0,0.0} \definecolor{cv1v5}{rgb}{0.0,0.0,0.0} \definecolor{cv1v6}{rgb}{0.0,0.0,0.0} \definecolor{cv1v13}{rgb}{0.0,0.0,0.0} \definecolor{cv2v4}{rgb}{0.0,0.0,0.0} \definecolor{cv2v5}{rgb}{0.0,0.0,0.0} \definecolor{cv2v12}{rgb}{0.0,0.0,0.0} \definecolor{cv3v4}{rgb}{0.0,0.0,0.0} \definecolor{cv3v11}{rgb}{0.0,0.0,0.0} \definecolor{cv4v10}{rgb}{0.0,0.0,0.0} \definecolor{cv5v18}{rgb}{0.0,0.0,0.0} \definecolor{cv6v17}{rgb}{0.0,0.0,0.0} \definecolor{cv6v8}{rgb}{0.0,0.0,0.0} \definecolor{cv7v16}{rgb}{0.0,0.0,0.0} \definecolor{cv7v18}{rgb}{0.0,0.0,0.0} \definecolor{cv8v15}{rgb}{0.0,0.0,0.0} \definecolor{cv8v17}{rgb}{0.0,0.0,0.0} \definecolor{cv10v15}{rgb}{0.0,0.0,0.0} \definecolor{cv10v13}{rgb}{0.0,0.0,0.0} \definecolor{cv11v12}{rgb}{0.0,0.0,0.0} \definecolor{cv11v14}{rgb}{0.0,0.0,0.0} \definecolor{cv12v18}{rgb}{0.0,0.0,0.0} \definecolor{cv12v13}{rgb}{0.0,0.0,0.0} \definecolor{cv13v17}{rgb}{0.0,0.0,0.0} \definecolor{cv14v16}{rgb}{0.0,0.0,0.0} \definecolor{cv16v18}{rgb}{0.0,0.0,0.0} % \Vertex[style={minimum size=1.0cm,draw=cv0,fill=cfv0,text=clv0,shape=circle},LabelOut=false,L=\hbox{$1$},x=4.3933cm,y=3.1742cm]{v0} \Vertex[style={minimum size=1.0cm,draw=cv1,fill=cfv1,text=clv1,shape=circle},LabelOut=false,L=\hbox{$2$},x=4.3473cm,y=2.4382cm]{v1} \Vertex[style={minimum size=1.0cm,draw=cv2,fill=cfv2,text=clv2,shape=circle},LabelOut=false,L=\hbox{$3$},x=2.7141cm,y=2.6372cm]{v2} \Vertex[style={minimum size=1.0cm,draw=cv3,fill=cfv3,text=clv3,shape=circle},LabelOut=false,L=\hbox{$4$},x=0.0cm,y=2.8939cm]{v3} \Vertex[style={minimum size=1.0cm,draw=cv4,fill=cfv4,text=clv4,shape=circle},LabelOut=false,L=\hbox{$5$},x=1.0586cm,y=1.9979cm]{v4} \Vertex[style={minimum size=1.0cm,draw=cv5,fill=cfv5,text=clv5,shape=circle},LabelOut=false,L=\hbox{$6$},x=3.8281cm,y=3.5334cm]{v5} \Vertex[style={minimum size=1.0cm,draw=cv6,fill=cfv6,text=clv6,shape=circle},LabelOut=false,L=\hbox{$7$},x=5.0cm,y=1.7711cm]{v6} \Vertex[style={minimum size=1.0cm,draw=cv7,fill=cfv7,text=clv7,shape=circle},LabelOut=false,L=\hbox{$8$},x=5.0cm,y=4.2583cm]{v7} \Vertex[style={minimum size=1.0cm,draw=cv8,fill=cfv8,text=clv8,shape=circle},LabelOut=false,L=\hbox{$9$},x=4.6513cm,y=0.488cm]{v8} \Vertex[style={minimum size=1.0cm,draw=cv9,fill=cfv9,text=clv9,shape=circle},LabelOut=false,L=\hbox{$10$},x=4.1959cm,y=4.6223cm]{v9} \Vertex[style={minimum size=1.0cm,draw=cv10,fill=cfv10,text=clv10,shape=circle},LabelOut=false,L=\hbox{$11$},x=1.9924cm,y=0.946cm]{v10} \Vertex[style={minimum size=1.0cm,draw=cv11,fill=cfv11,text=clv11,shape=circle},LabelOut=false,L=\hbox{$12$},x=1.2107cm,y=3.6788cm]{v11} \Vertex[style={minimum size=1.0cm,draw=cv12,fill=cfv12,text=clv12,shape=circle},LabelOut=false,L=\hbox{$13$},x=2.4701cm,y=3.1256cm]{v12} \Vertex[style={minimum size=1.0cm,draw=cv13,fill=cfv13,text=clv13,shape=circle},LabelOut=false,L=\hbox{$14$},x=3.1256cm,y=1.7896cm]{v13} \Vertex[style={minimum size=1.0cm,draw=cv14,fill=cfv14,text=clv14,shape=circle},LabelOut=false,L=\hbox{$15$},x=2.9151cm,y=4.1936cm]{v14} \Vertex[style={minimum size=1.0cm,draw=cv15,fill=cfv15,text=clv15,shape=circle},LabelOut=false,L=\hbox{$16$},x=3.0806cm,y=0.0cm]{v15} \Vertex[style={minimum size=1.0cm,draw=cv16,fill=cfv16,text=clv16,shape=circle},LabelOut=false,L=\hbox{$17$},x=4.0317cm,y=5.0cm]{v16} \Vertex[style={minimum size=1.0cm,draw=cv17,fill=cfv17,text=clv17,shape=circle},LabelOut=false,L=\hbox{$18$},x=4.5116cm,y=1.1085cm]{v17} \Vertex[style={minimum size=1.0cm,draw=cv18,fill=cfv18,text=clv18,shape=circle},LabelOut=false,L=\hbox{$19$},x=3.6613cm,y=4.1862cm]{v18} % \Edge[lw=0.1cm,style={color=cv0v2,},](v0)(v2) \Edge[lw=0.1cm,style={color=cv0v6,},](v0)(v6) \Edge[lw=0.1cm,style={color=cv0v7,},](v0)(v7) \Edge[lw=0.1cm,style={color=cv0v14,},](v0)(v14) \Edge[lw=0.1cm,style={color=cv1v5,},](v1)(v5) \Edge[lw=0.1cm,style={color=cv1v6,},](v1)(v6) \Edge[lw=0.1cm,style={color=cv1v13,},](v1)(v13) \Edge[lw=0.1cm,style={color=cv2v4,},](v2)(v4) \Edge[lw=0.1cm,style={color=cv2v5,},](v2)(v5) \Edge[lw=0.1cm,style={color=cv2v12,},](v2)(v12) \Edge[lw=0.1cm,style={color=cv3v4,},](v3)(v4) \Edge[lw=0.1cm,style={color=cv3v11,},](v3)(v11) \Edge[lw=0.1cm,style={color=cv4v10,},](v4)(v10) \Edge[lw=0.1cm,style={color=cv5v9,},](v5)(v9) \Edge[lw=0.1cm,style={color=cv5v18,},](v5)(v18) \Edge[lw=0.1cm,style={color=cv6v8,},](v6)(v8) \Edge[lw=0.1cm,style={color=cv6v17,},](v6)(v17) \Edge[lw=0.1cm,style={color=cv7v16,},](v7)(v16) \Edge[lw=0.1cm,style={color=cv7v18,},](v7)(v18) \Edge[lw=0.1cm,style={color=cv8v15,},](v8)(v15) \Edge[lw=0.1cm,style={color=cv8v17,},](v8)(v17) \Edge[lw=0.1cm,style={color=cv9v14,},](v9)(v14) \Edge[lw=0.1cm,style={color=cv9v16,},](v9)(v16) \Edge[lw=0.1cm,style={color=cv10v13,},](v10)(v13) \Edge[lw=0.1cm,style={color=cv10v15,},](v10)(v15) \Edge[lw=0.1cm,style={color=cv11v12,},](v11)(v12) \Edge[lw=0.1cm,style={color=cv11v14,},](v11)(v14) \Edge[lw=0.1cm,style={color=cv12v13,},](v12)(v13) \Edge[lw=0.1cm,style={color=cv12v18,},](v12)(v18) \Edge[lw=0.1cm,style={color=cv13v17,},](v13)(v17) \Edge[lw=0.1cm,style={color=cv14v16,},](v14)(v16) \Edge[lw=0.1cm,style={color=cv16v18,},](v16)(v18) % \end{tikzpicture}
True
graphs.BalancedTree(3,3).show()
Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1188, in execute flags=compile_flags), namespace, locals) File "<string>", line 1 ?mycielsk ^ SyntaxError: invalid syntax
g = graphs.RandomBarabasiAlbert(8,5) g.show()
g.pagerank()
{0: 0.10074809095806429, 1: 0.07327961278619403, 2: 0.10074809095806443, 3: 0.0734331428270892, 4: 0.07327961278619406, 5: 0.22412076774886017, 6: 0.1928113985715906, 7: 0.16157928336394337}
g.num_edges()
15