We show how one can trace in a systematic way the coarse-grained solutions of individual-based stochastic epidemic models evolving on heterogeneous complex networks with respect to their topological characteristics. In particular, we illustrate the "distinct" impact of the average path length (with respect to the degree and clustering distributions) on the emergent behavior of detailed epidemic models; to achieve this we have developed an algorithm that allows its tuning at will. The framework could be used to shed more light on the influence of weak social links on epidemic spread within small-world network structures, and ultimately to provide novel systematic computational modeling and exploration of better contagion control strategies.