  Let $G$ be a graph with edge set $E(G)$. Denote by $d_w$ the degree of a
vertex $w$ of $G$. The sigma index of $G$ is defined as $\sum_{uv\in
E(G)}(d_u-d_v)^2$. A connected graph of order $n$ and size $n+k-1$ is known as
a connected $k$-cyclic graph. Abdo, Dimitrov, and Gutman [Discrete Appl. Math.
250 (2018) 57-64] characterized the graphs having the greatest sigma index over
the family of all connected graphs of a fixed order. The primary goal of the
present note is to determine graphs possessing the greatest sigma index from
the class of all connected $k$-cyclic graphs of a fixed order.
