# Adding a vertex weight on top of a labeled vertex

I'm using tikz to draw my graph (a complete graph). I labeled the edges and the vertices and want to add the weight of each vertices on top of it. Here's what I've done:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{graphs,graphs.standard}

\begin{document}
\begin{tikzpicture}
\graph { subgraph K_n [n=3,clockwise,radius=2cm, nodes={circle,draw}] };
\draw (1) -- node[midway, above right] {4} (2);
\draw (1) -- node[midway, above left] {5} (3);
\draw (2) -- node[midway, below] {6} (3);
\end{tikzpicture}
\end{document}


The weights of each vertices that I want to add are: 10 on vertex 1, 12 on vertex 2, and 14 on vertex 3. Is there a way to do it? Thanks in advance.

By of pure tikz is simple:

\documentclass[border=3.141592]{standalone}
\usepackage{tikz}
\usetikzlibrary{positioning,
quotes}

\begin{document}
\begin{tikzpicture}[
node distance =24mm and 12mm,
C/.style = {circle, draw, minimum size=1em}
]
\node (v1) [C, label=10] {1};
\node (v2) [C, label=12, above right=of v1] {2};
\node (v3) [C, label=14, below right=of v2] {3};
%
\draw (v1)  to["4"] (v2)
to["6"] (v3)
to["5"] (v1);
\end{tikzpicture}
\end{document}


With use of LuaLaTeX and TikZ libraries graphs, graphdrawing and gdlibrary circular:

\documentclass[border=3.141592]{standalone}
\usepackage{tikz}
\usetikzlibrary{graphs,graphdrawing,
quotes}
\usegdlibrary {circular}

\begin{document}
\begin{tikzpicture}[
every label/.append style = {font=\small, text=blue}
]
\graph [simple necklace layout,
grow'=down, node sep=22mm,
nodes={draw,circle},
edges={auto, nodes={font=\scriptsize, inner sep=1pt}}
] {
1[label=10] --["4"] 2[label=12] --["6"] 3[label=14] --["5"] 1;
};
\end{tikzpicture}
\end{document}
`