We study the problem of the emergence of cooperation in dynamic signed networks where agent strategies coevolve with relational signs and network topology. Running simulations based on an agent-based model, we compare results obtained in a regular lattice initialization with those obtained on a comparable random network initialization. We show that the increased degree heterogeneity at the outset enlarges the parametric conditions in which cooperation survives in the long run. Furthermore, we show how the presence of sign-dependent emotional strategies catalyze the evolution of cooperation with both network topology initializations.