For a given set of queries (which are expressions in some query language) $\mathcal{Q}=\{Q_1$, $Q_2, \ldots Q_k\}$ and for another query $Q_0$ we say that $\mathcal{Q}$ determines $Q_0$ if -- informally speaking -- for every database $\mathbb D$, the information contained in the views $\mathcal{Q}({\mathbb D})$ is sufficient to compute $Q_0({\mathbb D})$. Query Determinacy Problem is the problem of deciding, for given $\mathcal{Q}$ and $Q_0$, whether $\mathcal{Q}$ determines $Q_0$. Many versions of this problem, for different query languages, were studied in database theory. In this paper we solve a problem stated in [CGLV02] and show that Query Determinacy Problem is undecidable for the Regular Path Queries -- the paradigmatic query language of graph databases.