My research interests lie primarily in algorithmic and computational aspects of graph theory, particularly for problems defined on directed, signed and mixed graphs. This includes applications in areas as wide ranging as quantum physics and social sciences. Within this framework I study homomorphisms and colourings, discrete-time processes and graph-searching models. In each of these areas I utilize tools from discrete mathematics, combinatorics and theoretical computer science to study computational questions such as asymptotic behaviours of evolving discrete systems, parameter bounds, and computational complexity. My research yields fundamental theorems and analyses that lay the groundwork for future applications of multi-layer graph models in the social and physical sciences.