Modelling interactions on complex networks needs efficient algorithms for describing processes on a detailed level in the network structure. This kind of modelling enables more realistic applications of spreading processes, network metrics, and analyses of communities. However, different real-world processes may impose requirements for implementations and their efficiency. We discuss different transmission and spreading processes and their interrelations. Two pseudo-algorithms are presented, one for the complex contagion-spreading mechanism using non-self-avoiding paths in the modelling, and one for simple contagion processes using self-avoiding paths in the modelling. The first algorithm is an efficient implementation that can be used for describing social interaction in a social network structure. The second algorithm is a less efficient implementation for describing specific forms of information transmission and epidemic spreading.