In this talk, we will discuss conditions under which a metric space is inner approximated by its computable subspaces. We focus on (generalised) topological graphs, which are spaces obtained by gluing arcs and rays together at their endpoints. First, we show that every non-vertex point in a semicomputable topological graph has a neighbourhood which is a computable arc with computable endpoints. Using this, we show that every semicomputable topological graph is inner approximated by computable topological graphs with computable endpoints. This talk is based on joint work with Vedran Čačić, Marko Horvat and Zvonko Iljazović.