Vtyjkyuk

Is there are way to rotate standard graphs in tikz?

For example, the following produces a cyclic graph with 6 vertices

begintikzpicture[every node/.style=fill,circle,very thick,inner sep=0pt]
 graph[clockwise, radius=2cm] subgraph C_n [n=6];
 endtikzpicture

Is there a way I can rotate this graph by a given angle?

Using rotate and transform shape you can rotate the graph any angle you choose.

documentclass[tikz,margin=0.5cm]standalone
usetikzlibrarygraphs
usetikzlibrarygraphs.standard
begindocument
begintikzpicture[every node/.style=fill,circle,very thick,inner sep=0pt] 
beginscope[rotate=15,transform shape]
graph[clockwise, radius=2cm] subgraph C_n [n=6]; 
endscope
endtikzpicture
enddocument

Just for testing, the graph generated by library Graphs actues as a node, when you use scope with the modificator rotate, only afects coordinates, to rotate each node you must declare the rotate value in each node style; the correct way is using trasform shape, here a test of these aspects included basic tikz code drawing, in red, and imported images in nodes using graphicx.

RESULT:

MWE: animation using imagemagik converter

% arara: pdflatex: synctex: yes, action: nonstopmode
% arara: animate: density: 150, delay: 15, other: -background white -alpha remove
% arara: showanimate
documentclass[tikz,margin=0.5cm]standalone
usetikzlibrarygraphs
usepackagegraphicx
usetikzlibrarygraphs.standard,calc
begindocument
foreach x in 0,1,...,29
 begintikzpicture[
 every node/.style=
 fill=blue!20,
 circle,
 very thick,
 inner sep=0pt,
 minimum size=12pt
 
 ] 
 pgfmathparseint(12*x)
 edefAnglepgfmathresult
 %Set image limits to avoid flickering
 draw(-3,4) rectangle (9,-9);
 draw(90:2.7) node[fill=none,font=scriptsize] Scope[rotate=0]
 ++(6,0) node[fill=none,font=scriptsize] Scope[rotate=Angle]
 ++(0,-6) node[fill=none,font=scriptsize] Scope[rotate=Angle,trasform shape]
 ++(-6,0) node[fill=none,font=scriptsize] Scope[rotate=0], each node[rotate=Angle];
 %basic drawing test
 beginscope[rotate=0] 
 %Graph generated objet
 graph[clockwise, radius=2cm] subgraph C_n [n=6];
 %Tikz basic code objet
 foreach n in 1,2,...,6
 node[fill=red!20](nn) at (60*n:1.5)n; 
 
 draw[red,->](n1) 
 -- (n2) -- node[midway,sloped,above=-10pt, font=tiny,fill=none]tikz objet (n3) -- (n4) 
 -- (n5) -- (n6) -- (n1);
 node[label=-90:tiny Angle] at (0:2.5cm) 0;
 %Graphicx Objet
 node at (0,0)includegraphics[width=1.5cm]example-image;
 node at (180:2.5cm)includegraphics[width=0.5cm]example-image-a; 
 endscope

 %test rotate
 beginscope[shift=(6,0),rotate=Angle]

 %Graph generated objet
 graph[clockwise, radius=2cm] subgraph C_n [n=6];
 %Tikz basic code objet
 foreach n in 1,2,...,6
 node[fill=red!20](nn) at (60*n:1.5)n; 
 
 draw[red,->](n1) 
 -- (n2) -- node[midway,sloped,above=-10pt, font=tiny,fill=none]tikz objet (n3) -- (n4) 
 -- (n5) -- (n6) -- (n1);
 node[label=-90:tiny Angle] at (0:2.5cm) Angle;
 %Graphicx Objet
 node at (0,0)includegraphics[width=1.5cm]example-image;
 node at (180:2.5cm)includegraphics[width=0.5cm]example-image-a; 
 endscope

 %test rotate nodes
 beginscope[shift=(0,-6),rotate=0]
 %Graph generated objet
 graph[clockwise, radius=2cm] subgraph C_n [n=6];
 %Tikz basic code objet
 foreach n in 1,2,...,6
 node[fill=red!20,rotate=Angle](nn) at (60*n:1.5)n; 
 
 draw[red,->](n1) 
 -- (n2) -- node[midway,sloped,above=-10pt, font=tiny,fill=none,rotate=Angle]tikz objet (n3) -- (n4) 
 -- (n5) -- (n6) -- (n1);
 node[label=-90:tiny Angle,rotate=Angle] at (0:2.5cm) Angle;
 %Graphicx Objet
 node at (0,0)includegraphics[width=1.5cm,angle=Angle]example-image;
 node at (180:2.5cm)includegraphics[width=0.5cm,angle=-Angle]example-image-a; 
 endscope

 %test 4 transform shape
 beginscope[shift=(6,-6),rotate=Angle, transform shape] 
 %Graph generated objet
 graph[clockwise, radius=2cm] subgraph C_n [n=6];
 %Tikz basic code objet
 foreach n in 1,2,...,6
 node[fill=red!20](nn) at (60*n:1.5)n; 
 
 draw[red,->](n1) 
 -- (n2) -- node[midway,sloped,above=-10pt, font=tiny,fill=none]tikz objet (n3) -- (n4) 
 -- (n5) -- (n6) -- (n1);
 node[label=-90:tiny Angle] at (0:2.5cm) Angle;
 %Graphicx Objet
 node at (0,0)includegraphics[width=1.5cm]example-image;
 node at (180:2.5cm)includegraphics[width=0.5cm]example-image-a; 
 endscope

 endtikzpicture

enddocument

You should look into the tkz-berge package. It is especially designed for graph theory and the rotation is easily set through the options.

documentclass[11pt,border=2pt]standalone
usepackagetkz-berge
begindocument
begintikzpicture
GraphInit[vstyle=Shade]
SetVertexNoLabel
grCycle[x=0,y=0, rotation=90]6
grCycle[x=10,y=0]6
endtikzpicture
enddocument

The output running in Gummi is:

Notice there is a command for cycles, grCycle, and in the options the placement of the first cycle is put at x=0 and y=0 and is rotated 90 degrees. Also notice there are specific looks you can make your graph have; the one below is Shade. There is also the option to label vertices inside or outside and to weight the arcs.

EDIT: I should also point out the "Gallery of Named Graphs" which is here. This includes 3 different representations of the Petersen graph, cages, and others not mentioned in the documentation of tkz-berge.