$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{with}\left(\mathrm{SpecialGraphs}\right)\:$

$G:=\mathrm{CycleGraph}\left({10}^5\right)\:$

$\mathrm{CodeTools}:-\mathrm{Usage}\left(\mathrm{DrawGraph}\left(G\right)\right)\:$

Maple 18: memory used=1.26GiB, alloc change=122.29MiB, cpu time=18.10s, real time=18.23s, gc time=7.25s (Windows)

Maple 17: Runs out of memory

Mathematica^® 9: AbsoluteTiming[GraphPlot[CycleGraph[10^5]]] gives 27.597759 s

$\mathrm{G1}:=\mathrm{Graph}\left(\mathrm{directed}\,\mathrm{Trail}\left(1\,2\,3\,1\,4\,5\right)\right)$

$\mathrm{G1}:=\mathrm{Graph\; 1:\; a\; directed\; unweighted\; graph\; with\; 5\; vertices\; and\; 5\; arc(s)}$

$\mathrm{G2}:=\mathrm{Graph}\left(\mathrm{directed}\,\mathrm{Trail}\left(1\,2\,3\,4\,5\,3\right)\right)$

$\mathrm{G2}:=\mathrm{Graph\; 2:\; a\; directed\; unweighted\; graph\; with\; 5\; vertices\; and\; 5\; arc(s)}$

$\mathrm{G3}:=\mathrm{Graph}\left(\mathrm{directed}\,\mathrm{Trail}\left(3\,4\,5\,3\,1\,2\right)\right)$

$\mathrm{G3}:=\mathrm{Graph\; 3:\; a\; directed\; unweighted\; graph\; with\; 5\; vertices\; and\; 5\; arc(s)}$

$\mathrm{DrawGraph}\left(\left[\mathrm{G1}\,\mathrm{G2}\,\mathrm{G3}\right]\,\mathrm{width}\=3\,\mathrm{style}\=\mathrm{circle}\right)$

$\mathrm{IsIsomorphic}\left(\mathrm{G1}\,\mathrm{G2}\right)$

$\mathrm{false}$

$\mathrm{IsIsomorphic}\left(\mathrm{G2}\,\mathrm{G3}\right)$

$\mathrm{false}$

$\mathrm{IsIsomorphic}\left(\mathrm{G1}\,\mathrm{G3}\,\'\mathrm{\φ}\'\right)$

$\mathrm{true}$

$\mathrm{\φ}$

$\left[1\=3\,2\=4\,3\=5\,4\=1\,5\=2\right]$

$G:=\mathrm{Graph}\left(\mathrm{directed}\,\mathrm{Trail}\left(a\,b\,c\,a\right)\,\mathrm{Trail}\left(d\,e\,f\right)\,\mathrm{Trail}\left(g\,h\,g\right)\right)$

$G:=\mathrm{Graph\; 4:\; a\; directed\; unweighted\; graph\; with\; 8\; vertices\; and\; 7\; arc(s)}$

$H:=\mathrm{Graph}\left(\mathrm{directed}\,\mathrm{Trail}\left(a\,b\,a\right)\,\mathrm{Trail}\left(c\,d\,e\,c\right)\,\mathrm{Trail}\left(f\,g\,h\right)\right)$

$H:=\mathrm{Graph\; 5:\; a\; directed\; unweighted\; graph\; with\; 8\; vertices\; and\; 7\; arc(s)}$

$\mathrm{DrawGraph}\left(\left[G\,H\right]\,\mathrm{width}\=2\,\mathrm{style}\=\mathrm{circle}\right)$

$\mathrm{IsIsomorphic}\left(G\,H\,\'\mathrm{\φ}\'\right)$

$\mathrm{true}$

$\mathrm{\φ}$

$\left[a\=c\,b\=d\,c\=e\,d\=f\,e\=g\,f\=h\,g\=a\,h\=b\right]$

Commands: IsIsomorphic (Maple 18) versus IsomorphicGraphQ (Mathematica^® 9)

Small: Random directed unweighted graph with 10 vertices and 20 arc(s)

Medium: Random directed unweighted graph with 100 vertices and 200 arc(s)

Large: Random directed unweighted graph with 987 vertices and 2000 arc(s)

$S:=\mathrm{SoccerBallGraph}\left(\right)$

$S:=\mathrm{Graph\; 1:\; an\; undirected\; unweighted\; graph\; with\; 60\; vertices\; and\; 90\; edge(s)}$

$\mathrm{DrawGraph}\left(S\right)$

$\mathrm{Latex}\left(S\,\mathrm{FileTools}:-\mathrm{JoinPath}\left(\left[\mathrm{FileTools}:-\mathrm{TemporaryDirectory}\left(\right)\, ''soccer.tex''\right]\right)\,300\,300\,\mathrm{true}\right)$

$\mathrm{lstring}:=\mathrm{Latex}\left(S\,''''\,300\,300\,\mathrm{true}\,\'\mathrm{pictureonly}\'\=\mathrm{true}\right)\:$

$\mathrm{printf}\left(''\%.1500s...''\,\mathrm{lstring}\right)$

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