How to add shading to a node in a graph

documentclass{beamer}
usepackage{tikz}
usetikzlibrary{arrows.meta, shadows}%<---------------add shadow
%usepackage{default}
begin{document}
begin{frame}
begin{tikzpicture}
node[shape=circle,draw=black,fill=white, drop shadow] (A) at (0,2) {A};
node[shape=circle,draw=black,fill=white, drop shadow] (B) at (0,0) {B};
path (A) edge [loop above] node {} (A);
path (B) edge   [->]           node[above] {} (A);
end{tikzpicture}
end{frame}
end{document}

EDIT -- for better control over shading

You can also have better control over the color shading by adding the following line to the options of any node in []

drop shadow={top color=green,
                bottom color=yellow!40,
                shadow xshift=4pt,
                shadow yshift=-4pt,}

Similarly the xshift and yshift give more precise control over the shadow placement

An example is reproduced below--- note-- the shadows can be applied to arrows also

documentclass{beamer}
usepackage{tikz}
usetikzlibrary{arrows.meta, shadows, shadows.blur}
%usepackage{default}
begin{document}
begin{frame}
begin{tikzpicture}
node[shape=circle,
        draw=black,
        fill=white, 
        drop shadow={top color=blue,
                    bottom color=blue!40,
                    shadow xshift=2pt,
                    shadow yshift=-2pt,}, 
%       blur shadow={shadow blur steps=1}
        ] 
        (A) at (0,2) {A};
node[shape=circle,
        draw=black,
        fill=white, 
        drop shadow={top color=green,
                    bottom color=yellow!40,
                    shadow xshift=4pt,
                    shadow yshift=-4pt,}, 
%       blur shadow={shadow blur steps=1}
    ]  
        (B) at (0,0) {B};
path (A) edge [loop above] node {} (A);
path (B) edge   [->]           node[above] {} (A);
end{tikzpicture}
end{frame}
end{document}