A parameterized tropical curve in $B$ is a continuous map

$$h:\Gamma\rightarrow B$$

where $\Gamma$ is obtained from a graph $\overline{\Gamma}$ as above, satisfying the following two properties:

1. (1)

   If $E\in\Gamma^{[1]}$ and $w(E)=0$, then $h|_{E}$ is constant; otherwise $h|_{E}$ is a proper embedding of $E$ into $B$ as a line segment, ray or line of rational slope.

2. (2)

   The balancing condition. Let $V\in\overline{\Gamma}^{[0]}$ be a vertex with valency larger than $1$, with adjacent edges $E_{1},\ldots,E_{\ell}$. Let $v_{i}\in\Lambda_{h(V)}$ be a primitive tangent vector to $h(E_{i})$ at $h(V)$, pointing away from $h(V)$. Then

   $$\sum_{i=1}^{\ell}w(E_{i})v_{i}=0.$$