  Being motivated in terms of mathematical concepts from the theory of
electrical networks, Klein & Ivanciuc introduced and studied a new
graph-theoretic cyclicity index--the global cyclicity index (Graph cyclicity,
excess conductance, and resistance deficit, J. Math. Chem. 30 (2001) 271--287).
In this paper, by utilizing techniques from graph theory, electrical network
theory and real analysis, we obtain some further results on this new cyclicity
measure, including the strictly monotone increasing property, some lower and
upper bounds, and some Nordhuas-Gaddum-type results. In particular, we
establish a relationship between the global cyclicity index $C(G)$ and the
cyclomatic number $\mu(G)$ of a connected graph $G$ with $n$ vertices and $m$
edges: $$\frac{m}{n-1}\mu(G)\leq C(G)\leq \frac{n}{2}\mu(G).$$
