Doesn't every undirected graph have a cycle (eg, $a$-$b$-$a$ for nodes $a$ and $b$ joined by an edge)? Why there is no circular path in every undirected-graph?
For example: Given 2 nodes a & b and one undirected edge that connects them
There is a cycle graph a-b-a
Plus,What's the exact definition of circular path?
 A: Path: A string of alternating vertices and edges $v_1e_1v_2e_2\dots v_{n-1}e_{n-1}v_n$, ($n\geq 2$) is said to be a path if no vertex repeat.
Circular path: A string of alternating vertices edges $v_1e_1v_2e_2\dots v_{n-1}e_{n-1}v_n$, ($n\geq 2$) is said to be a circular path if no vertex repeat exept for $v_1=v_n$ and no edge repeat.
Now if the graph has parallel edges $e_1$ and $e_2$ joining two vertex $u$ and $v$. Then $ue_1ve_2u$ is a circular path of size $2$. But for simple graph since there is no parallel edge so there is no circular path of size $2$. Because in this case edges will repeat.
Now most of the books concern only simple graphs, so they do not include the "no edge repeat" part. But for a non simple graph it is required to mention that. Otherwise for $n=2$ an ambiguity occurs what you have mentioned.
In your question you have not said the graph is simple or not. But since you have not mention edge, so $ab$ and $ba$ are same edges. So here the edge is repeating, so $aba$ is not a circular path.
