A metric graph is a metric space obtained from a finite collection
of intervals whose endpoints are identified in groups.
It can also be seen as a finite, edge-weighted graph where the continuum of points along the interior
of each edge is taken into consideration, and each edge is locally isometric to an interval whose
length is the edge-weight. The diameter of a metric graph $G$ is the maximum distance between all pairs of points of $G$.
We show that the total length of a metric graph $G$ with $\leaves(G)$ leaves,
cyclomatic number $\cyc(G)$, and diameter $\diam(G)$ is at most
$\big(\cyc(G) + \max\big\{1, \leaves(G)/2 \big\}\big) \cdot \diam(G)$. Furthermore,
we show that this bound is tight, and we characterize the metric graphs where equality holds.
As an application, we provide tight bounds in certain cases for the diameter of metric graphs
obtained from a cycle or a star by the identification of a fixed number of points (pairwise or in groups).
