Mindmap creates connection line composed of the parent/child colors. Is it possible to apply such effect on normal parent/child trees to connect the parent and child nodes with a gradient of their corresponding colors? In a basic example of
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes,trees}
\begin{document}
\begin{tikzpicture}
\node[circle,fill=blue] (par) at (0,0) {Parent}
[level distance=4cm,sibling angle=25,clockwise from=80]
child {node[circle,fill=red] (child1) {Child 1}}
child {node[circle,fill=yellow] (child2) {Child 2}}
child {node[circle,fill=green] (child3) {Child 3}};
\end{tikzpicture}
\end{document}

How to make a gradient of blue ... red for the line connecting the parent to the first child, blue ... yellow for the second child, etc.