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I am trying to draw the following image in Tikz

But all I got is

I am not able to make it into a perfect circle. The code is

 documentclass[tikz,border=2mm]standalone 
 begindocument
 begintikzpicture
 coordinate (O) at (0,0);
 coordinate (A) at (60:1cm);
 coordinate (B) at (180:1cm);
 coordinate (C) at (300:1cm);
 node at (O) $+1$; 
 node at (A) $1$; 
 node at (B) $2$; 
 node at (C) $3$;

 draw[->] (A) to [bend right] (B);
 draw[->] (B) to [bend right] (C);
 draw[->] (C) to [bend right] (A); 
 endtikzpicture
 endfigure* 
 enddocument

Thanks is advance.

Using tkz-euclide :

documentclass[border=3mm]standalone
usepackagetkz-euclide
usetkzobjall
begindocument
begintikzpicture
 tkzDefPoint(0,0)O
 tkzDefPoint(60:1)A
 tkzDefPoint(180:1)B
 tkzDefPoint(300:1)C

 tikzsetcompass style/.append style=orange,line width=0.7mm,-stealth
 tkzDrawArc[delta=-10](O,A)(B) 
 tkzDrawArc[delta=-10](O,B)(C)
 tkzDrawArc[delta=-10](O,C)(A)

 node[orange] at (O) textbf+1; 
 node[blue] at (A) textbf1; 
 node[blue] at (B) textbf2;
 node[blue] at (C) textbf3;

 endtikzpicture
enddocument 

Just for fun: with arcs that really run around the circle and do not require any hard coded angles, i.e. the arcs adjust to the sizes of the nodes since their end points are computed from intersections of the circle with the node boundaries. The code is more or less taken from here. Note also that the arrow heads are bent.

documentclass[border=5mm,tikz]standalone
usetikzlibraryarrows.meta,bending,calc,intersections
begindocument
begintikzpicture[nodes=circle,text=blue,execute at begin node=$,
execute at end node=$,
 pics/circular arc/.style args=from #1 to #2code=
 path[name path=arc] 
 let p1=(#1),p2=(#2),n1=Mod(720+atan2(y1,x1),360),
 n2=Mod(720+atan2(y2,x2),360),
 n3=ifthenelse(abs(n1-n2)<180,n2,n2+360)
 in (n1:r) arc(n1:n3:r);
 draw[pic actions,
 name intersections=of=#1 and arc,by=arcstart,
 name intersections=of=#2 and arc,by=arcend] 
 let p1=(arcstart),p2=(arcend),n1=Mod(720+atan2(y1,x1),360),
 n2=Mod(720+atan2(y2,x2),360),
 n3=ifthenelse(abs(n1-n2)<180,n2,n2+360)
 in (n1:r) arc(n1:n3:r);
 ]
defr1
% 3 nodes with possibly different sizes
path
(0:r) node[name path=p1] (p1) 1
(120:r) node[name path=p2] (p2) 2
(240:r) node[name path=p3] (p3) 3
(0,0) node[orange]+1;
beginscope[thick,orange,-Stealth[bend]]
 path piccircular arc=from p1 to p2
 piccircular arc=from p2 to p3
 piccircular arc=from p3 to p1;
endscope
beginscope[xshift=4cm]
path
(0:r) node[name path=p1] (p1) 1
(120:r) node[name path=p2] (p2) 2
(240:r) node[name path=p3] (p3) 3
(0,0) node[red] -1;
beginscope[thick,red,Stealth[bend]-]
 path piccircular arc=from p1 to p2
 piccircular arc=from p2 to p3
 piccircular arc=from p3 to p1;
endscope
endscope
endtikzpicture
enddocument

Or everything in one pic. Then it suffices to say e.g.

path (-2,2) pic[circular diagram/arcs=orange]circular diagram=1,2,3
node[orange]$+1$;

Full MWE:

documentclass[border=5mm,tikz]standalone
usetikzlibraryarrows.meta,bending,calc,intersections
begindocument
begintikzpicture[nodes=circle,
 pics/circular arc/.style args=from #1 to #2code=
 path[name path=arc] 
 let p1=(#1),p2=(#2),n1=Mod(720+atan2(y1,x1),360),
 n2=Mod(720+atan2(y2,x2),360),
 n3=ifthenelse(abs(n1-n2)<180,n2,n2+360)
 in (n1:pgfkeysvalueof/tikz/circular diagram/radius) arc(n1:n3:pgfkeysvalueof/tikz/circular diagram/radius);
 draw[pic actions,
 name intersections=of=#1 and arc,by=arcstart,
 name intersections=of=#2 and arc,by=arcend] 
 let p1=(arcstart),p2=(arcend),n1=Mod(720+atan2(y1,x1),360),
 n2=Mod(720+atan2(y2,x2),360),
 n3=ifthenelse(abs(n1-n2)<180,n2,n2+360)
 in (n1:pgfkeysvalueof/tikz/circular diagram/radius) arc(n1:n3:pgfkeysvalueof/tikz/circular diagram/radius);
 ,
pics/circular diagram/.style=code=
foreach XX [count=YY starting from 1] in #1
xdefmydimYY;
path foreach XX [count=YY starting from 0] in #1
(pgfkeysvalueof/tikz/circular diagram/offset angle+YY*360/mydim:%
pgfkeysvalueof/tikz/circular diagram/radius) node[name path=aux-YY] (aux-YY) XX ;
path[circular diagram/parc] foreach XX [evaluate=XX as YY using int(mod(XX+1,mydim))]
in 0,...,thenumexprmydim-1
piccircular arc=from aux-XX to aux-YY 
;,circular diagram/.cd,offset angle/.initial=0,radius/.initial=1,
parc/.style=thick,-Stealth[bend],
arcs/.code=tikzsetcircular diagram/parc/.append style=#1
]
path (-2,2) pic[circular diagram/arcs=orange]circular diagram=1,2,3
 node[orange]$+1$
 (2,2) pic[circular diagram/arcs=red,Stealth[bend]-]circular diagram=1,2,3
 node[red]$-1$
 (-2,-2) pic[circular diagram/.cd,arcs=purple,offset angle=45]circular
 diagram=$a$,$b$,$c$,$d$
 node[purple]$+1$
 (2,-2) pic[circular diagram/arcs=cyan,Stealth[bend]-]circular
 diagram=$a$,$b$,$c$,$d$
 node[cyan]$-1$;
endtikzpicture
enddocument

The following uses a static 8 degrees clearance on the circle around the nodes. Therefore it works good for the current node contents, but one might have to make adjustments to make it really fit ones use case (or someone might come up with an algorithmic way to calculate this).

documentclass[border=3.14,tikz]standalone

begindocument
begintikzpicture
 node $+1$;
 foreach[count=n]x in -60, 60, 180
 
 node (n) at (x:1) $n$;
 draw[<-] (x+8:1) arc[start angle=x+8, end angle=x+112, radius=1cm];
 
endtikzpicture
enddocument

Purely for comparison (and because it made an interesting exercise in loops) here is a version done in Metapost using the luamplib package.

Source

Compile with lualatex.

documentclass[border=5mm]standalone
usepackageluatex85
usepackageluamplib
begindocument
mplibtextextlabelenable
beginmplibcode
beginfig(1);
path c[];
c[+1] = fullcircle rotated -60 scaled 55;
c[-1] = c[+1] shifted 78 right;

color s[];
s[+1] = 7/8 (red + 1/2 green);
s[-1] = 3/4 red;

for n=-1, +1:
 for i=0 upto 2:
 numeric p, q;
 p = 8/3i;
 q = 8/3(i+n);
 label("$" & decimal (i+1) & "$", point p of c[n]) withcolor 2/3 blue;
 drawarrow subpath(p, q) of c[n] 
 cutbefore fullcircle scaled 14 shifted point p of c[n]
 cutafter fullcircle scaled 14 shifted point q of c[n]
 withcolor s[n];
 endfor
 label("$" if n>0: & "+" fi & decimal n & "$", center c[n]) withcolor s[n];
endfor

endfig;
endmplibcode
enddocument

A pstricks solution:

 documentclass[svgnames, border =2cm]standalone

 usepackagepst-node, pst-eucl, multido, auto-pst-pdf

 begindocument

 sffamilybfseries
 beginpspicture(-2,-2)(2,2)
 pssetlinewidth=1.5pt, arrowinset=0.12, nodesep =4pt
 multidoi=1+1, iangle=-60 + 120, iangles=-54+121, ianglet=53+1203%
 rput(1.5; iangle)rnodeNicolorRoyalBlueipnode(1.5; iangles)Sipnode(1.5; ianglet)Ti%
 pstArcOAB[linecolor=Gold, arrows= <-]OSiTi%
 rput(0,0)colorGold +1
 %
 endpspicture
 beginpspicture(-2,-2)(2,2)
 pssetlinewidth=1.5pt, arrowinset=0.12, nodesep =4pt
 multidoi=1+1, iangle=-60 + 120, iangles=-54+121, ianglet=54+1203%
 rput(1.5; iangle)rnodeNicolorRoyalBlueipnode(1.5; iangles)Sipnode(1.5; ianglet)Ti%
 pstArcOAB[linecolor=Crimson, arrows=->]OSiTi%
 rput(0,0)colorCrimson --1
 %
 endpspicture

 enddocument