Q: Can I draw a path using the `--` syntax but still something like `bend right`? I like the \draw (a) edge[bend right] (b) ; way of drawing because it allows me to curve the edge a bit without worrying about specific control points.
I like the \draw (a) -- (b) -- (c) ; way of drawing because it's helpful for drawing a sequence of edges in a graph.
Can I combine these somehow to bend the edges using the -- syntax?
\begin{tikzpicture}[every node/.style={draw,fill,circle}]

% straight line edges, annoying repetition of "(b)"
\node (a) at (1,4) {} ;  \node (b) at (2,4) {} ;  \node (c) at (3,4.5) {} ;
\draw (a) edge (b) ;   \draw (b) edge (c) ;

% just curve one of them it a bit
\node (a) at (1,3) {} ;  \node (b) at (2,3) {} ;  \node (c) at (3,3.5) {} ;
\draw (a) edge[bend right] (b) ;   \draw (b) edge (c) ;

% straight lines also, less redundant
\node (a) at (1,2) {} ;  \node (b) at (2,2) {} ;  \node (c) at (3,2.5) {} ;
\draw (a) -- (b) -- (c) ;

% i want to do something like this
%\node (a) at (1,1) {} ;  \node (b) at (2,1) {} ;  \node (c) at (3,1) {} ;
%\draw (a) -- [bend right] (b) -- (c) ;

\end{tikzpicture}

I know that I can use control points, other constructs to get a curved path, but I want something that doesn't involve coordinates other than the \nodes so I can move the \nodes around

A: Something like this?
\documentclass[tikz]{standalone}
\begin{document}
\begin{tikzpicture}[every node/.style={draw,fill,circle}]

% straight line edges, annoying repetition of "(b)"
\node (a) at (1,4) {} ;  \node (b) at (2,4) {} ;  \node (c) at (3,4.5) {} ;
\draw (a) edge (b) ;   \draw (b) edge (c) ;

% just curve one of them it a bit
\node (a) at (1,3) {} ;  \node (b) at (2,3) {} ;  \node (c) at (2,2) {} ;
\draw (a.center) to[bend right] (b.center) -- (c.center) ;

\end{tikzpicture}
\end{document}

