Tikz Path Highlighting

\newcommand{\convexpath}[2]{
[   
    create hullnodes/.code={
        \global\edef\namelist{#1}
        \foreach [count=\counter] \nodename in \namelist {
            \global\edef\numberofnodes{\counter}
            \node at (\nodename) [draw=none,name=hullnode\counter] {};
        }
        \node at (hullnode\numberofnodes) [name=hullnode0,draw=none] {};
        \pgfmathtruncatemacro\lastnumber{\numberofnodes+1}
        \node at (hullnode1) [name=hullnode\lastnumber,draw=none] {};
    },
    create hullnodes
]
($(hullnode1)!#2!-90:(hullnode0)$)
\foreach [
    evaluate=\currentnode as \previousnode using \currentnode-1,
    evaluate=\currentnode as \nextnode using \currentnode+1
    ] \currentnode in {1,...,\numberofnodes} {
  let
    \p1 = ($(hullnode\currentnode)!#2!-90:(hullnode\previousnode)$),
    \p2 = ($(hullnode\currentnode)!#2!90:(hullnode\nextnode)$),
    \p3 = ($(\p1) - (hullnode\currentnode)$),
    \n1 = {atan2(\y3,\x3)},
    \p4 = ($(\p2) - (hullnode\currentnode)$),
    \n2 = {atan2(\y4,\x4)},
    \n{delta} = {-Mod(\n1-\n2,360)}
  in 
    {-- (\p1) arc[start angle=\n1, delta angle=\n{delta}, radius=#2] -- (\p2)}
}
-- cycle
}



\begin{tikzpicture}

	\begin{pgfonlayer}{nodelayer}
		\node [style=white node] (1) at (0, 0) {};
		\node [style=black node] (2) at (-2, 0) {};
		\node [style=black node] (3) at (2, 0) {};
    % ........
	\end{pgfonlayer}
  
	\begin{pgfonlayer}{edgelayer}
		\draw (1) to (3);
		\draw (2) to (1);
		\draw (2) to (4);
		% .......
	\end{pgfonlayer}
  
	\begin{pgfonlayer}{background}
	\fill[cyan,opacity=1] \convexpath{1,2}{8pt};
	\fill[cyan,opacity=1] \convexpath{2,4}{8pt};	
	\fill[cyan,opacity=1] \convexpath{2,5,6,7,8,9,10}{8pt};		
  % ...... 
	\end{pgfonlayer}
  
\end{tikzpicture}