The behavior and stability of over-the-counter markets is of central concern to regulators. Little is known, however, about how the structure of these markets determine their properties. In this paper we consider an over-the-counter market populated by boundedly rational heterogeneous traders in which the structure is represented by a network. Stability if found to decrease as the market becomes less well connected. The valuations of traders in weakly connected markets diverge more frequently resulting in complex price dynamics. Small-world links and an above average number of undamentalist traders are also both shown to exacerbate instability.