Structural analysis of variable topology mechanisms (VTMs) is the leading task when studying the topological variability of mechanisms. Of several major concerns, structure decomposition and homomorphism identification are two dominating issues for the structural analysis of VTMs. This paper presents a systematic computational approach for the structure decomposition and homomorphism identification of planar VTMs. Along with the proposed method, a constraint matrix representation, that records the potential motion constraints and the topological structures of a VTM, is introduced for serving as the basis of the approach. In addition, a new index, namely, degrees of homomorphism (DOHs), is suggested for quantifying the topological similarity among VTMs. For illustration, an automatic steel clamping and sawing mechanism and a group of mechanisms with similar topologies are adopted, from which their structure decomposition and homomorphism identification are carried out. As shown, the method is both symbolically readable and computationally considerable. The result is helpful for the automated structural analysis and synthesis of variable topology mechanisms.