Cfrgtkky

How do I make the edges in the tree have same length and have some good symmetry? It looks kinda ugly.

It needs to look more symmetric.
Is there a simple way to achieve this goal?

begin{figure}[h]

    begin{tikzpicture}[

    > = stealth, 

    shorten > = 1pt,

    auto,

    node distance = 2cm, 

    semithick % line style

    ]



    tikzstyle{state}=[

    draw = black,

    thick,

    fill = white,

    minimum size = 4mm

    ]



    node[state][circle, draw](hub) {$hub$};        

    node[state][circle, draw] (a) [below left of=hub] {$a$};

    node[state][circle, draw] (b) [below right of=hub] {$b$};



    node[state][circle, draw] (c) [below left of=a] {$c$};        

    node[state][circle, draw] (d) [right of=c] {$d$};



    node[state][circle, draw] (e) [below left of=c] {$e$};        

    node[state][circle, draw] (f) [right of=e] {$f$};



    node[state][circle, draw] (g) [right of=d] {$g$};        

    node[state][circle, draw] (h) [right of=g] {$h$};





    path[->] (a) edge node {100} (hub);

    path[->] (b) edge node {85} (hub);       



    path[->] (c) edge node {35} (a);

    path[->] (d) edge node {55} (a);       

    path[->] (e) edge node {10} (c);

    path[->] (f) edge node {15} (c);   

    path[->] (g) edge node {40} (b);

    path[->] (h) edge node {25} (b);           





    node[state][circle, draw] (u) [above left of=hub] {$u$}; 

    node[state][circle, draw] (v) [above right of=hub] {$v$};



    node[state][circle, draw] (w) [above left of=u] {$w$}; 

    node[state][circle, draw] (x) [right of=w] {$x$}; 

    node[state][circle, draw] (y) [right of=x] {$y$};

    node[state][circle, draw] (z) [right of=y] {$z$};





    path[->] (hub) edge node {125} (u); 

    path[->] (hub) edge node {25} (v); 

    path[->] (u) edge node {50} (w);

    path[->] (u) edge node {60} (x);

    path[->] (v) edge node {10} (y);

    path[->] (v) edge node {12} (z);







    draw (0,-6) node[above,xshift=0.7cm]{$ textsc{Pos and Neg heap represented together as a single structure}$};

    end{tikzpicture}

end{figure}

May I advertize the forest package for this? Your symmetry concern is taken care of by a single key: calign=fixed edge angles. And it is much easier to punch in the tree, and to customize it.

documentclass[tikz,border=3.14mm]{standalone}

usepackage[edges]{forest}

begin{document}

begin{forest}

for tree={calign=fixed edge angles,

edge+={stealth-},grow=south,circle,draw,thick}

[$hub$

 [$a$,edge label={node[midway,left]{100}}

  [$c$,edge label={node[midway,left]{35}}

   [$e$,edge label={node[midway,left]{10}}]

   [$f$,edge label={node[midway,right]{15}}]

   ]

  [$d$,edge label={node[midway,right]{55}}]

  ]

 [$b$,edge label={node[midway,right]{85}}

  [$g$,edge label={node[midway,left]{40}}]

  [$h$,edge label={node[midway,right]{25}}]

 ]

]

end{forest}

end{document}

by help of tikz libraries arrows.meta, positioning and quotes:

documentclass[tikz, margin=3mm]{standalone}

usetikzlibrary{arrows.meta, 

                positioning, 

                quotes}



begin{document}

begin{tikzpicture}[

                  node distance = 6mm and 4mm,

       every edge/.append style = {draw, semithick, shorten >=1pt, -Stealth},

every edge quotes/.append style = {font=footnotesize, auto, inner sep=1pt},

            state/.append style = {circle, draw, minimum size = 5mm, 

                                   inner sep=1pt, outer sep=0pt} 

                    ]

%%%% below

node[state] (hub) {textit{hub}};

node[state] (a) [below left =12mm and 8mm of hub]  {$a$};

node[state] (c) [below left = of a]    {$c$};

node[state] (e) [below left = of c]    {$e$};

    node[state] (d) [below right = of a] {$d$};

    node[state] (f) [below right = of c] {$f$};

%

node[state] (b) [below right =12mm and 8mm of hub]     {$b$};

node[state] (h) [below right = of b]       {$h$};

    node[state] (g) [below left = of b]    {$g$};

%%%% above

node[state] (u) [above left =12mm and 8mm of hub]  {$u$};

node[state] (w) [above left = of u]    {$w$};

    node[state] (x) [above right = of u]   {$x$};

%

node[state] (v) [above right =12mm and 8mm of hub] {$v$};

node[state] (z) [above right = of v]   {$z$};

    node[state] (y) [above left = of v]    {$y$};

%%%% edges

path   (a) edge  ["100"] (hub)

    (b) edge  ["85"] (hub)



    (c) edge  ["35"]    (a)

    (d) edge  ["55" ']  (a)

    (e) edge  ["10"]    (c)

    (f) edge  ["15" ']  (c)

    (g) edge  ["40"]    (b)

    (h) edge  ["25" ,]  (b)



    (hub) edge  ["125"] (u)

    (hub) edge  ["25" '](v)

    (u) edge  ["50"]    (w)

    (u) edge  ["60" ']  (x)

    (v) edge  ["10"]    (y)

    (v) edge  ["12" ']  (z);

node[below=of hub |- e]

    {textsc{Pos and Neg heap represented together as a single structure}};

end{tikzpicture}

end{document}