equivalent to a CW complex. Refining this, Ghrist [@G] showed that $\operatorname{Conf}_n(G)$ is homotopy equivalent to a CW complex whose dimension at most the number of vertices of $G$ of degree at least 3. Our result therefore represents one of the (many) similarities between sink configuration spaces and classical configuration spaces of graphs. One notable fact about both Theorem \[fcm\] and the theorem of Ghrist is that the dimension of these spaces are bounded independent of $n$. While it is known that configuration spaces of manifolds can have cellular models (see [@FH]), these models do not usually have dimension which is independent of $n$.\
Following this construction, we will be able to prove many topological facts about sink configuration spaces. For instance, this model will easily allow us to compute the Euler characteristic of $\operatorname{Conf}_n^{\operatorname{sink}}(G,V)$ (see Corollary \[eulerchar\]) and prove that these spaces are $K(\pi,1)$ (see Theorem \[kpi1\]). Perhaps more substantially, we will also be able to compute the fundamental group of $\operatorname{Conf}_n^{\operatorname{sink}}(G,V)$ whenever $G$ is a tree.\

\[treepi1\] Let $G$ be a tree with vertex set $V$ and edge set $E$. Then $\pi_1(\operatorname{Conf}_n^{\operatorname{sink}}(G,V))$ admits a presentation with $|E|\cdot((n-2)2^{n-1}+1)$ many generators, whose every relation is a commutator. If $G$ is 