Let $G$ be a finite graph with vertex set $V(G)$ and edge set $E(G)$, and let $M(G)$ denote the cycle matroid of $G$ on ground set $E(G)$. For each subset $A \subset E(G)$, let $c(A)$ denote the number of connected components of the spanning subgraph $(V(G), A)$. Then the rank function $r_{M(G)}$ of $M(G)$ satisfies