In this paper, we create a matrix representation for spiking neural P systems with structural plasticity (SNPSP, for short), taking inspiration from existing algorithms and representations for related variants. Using our matrix representation, we provide a simulation algorithm for SNPSP systems. We prove that the algorithm correctly simulates an SNPSP system: our representation and algorithm are able to capture the syntax and semantics of SNPSP systems, e.g. plasticity rules, dynamism in the synapse set. Analyses of the time and space complexity of our algorithm show that its implementation can benefit using parallel computers. Our representation and simulation algorithm can be useful when implementing SNPSP systems and related variants with a dynamic topology, in software or hardware.