Previous work [J. Gómez-Gardeñes, S. Gómez, A. Arenas, and Y. Moreno, Phys. Rev. Lett. 106, 128701 (2011)] has reported that explosive synchronization can be achieved in heterogeneous networks with a microscopic correlation between the structural and dynamical properties of the networks. This phenomenon, however, cannot be observed in all heterogeneous networks even if this structure-dynamics correlation is preserved. It is therefore of particular interest to identify the general topological factors that can induce the first order synchronization transition and to understand the underlying mechanisms. Here we investigate this issue using the scenario of the smooth transformation from homogeneous Erdös-Rènyi networks to heterogeneous Barabàsi-Albert networks. Specifically, we scrutinize how local and global properties of the network change during this process, and how these properties are associated with the emergence of explosive synchronization. We find that the local degree-degree correlation in the network contributes primarily to explosive synchronization, other than the global topological property or starlike subgraphs. We furthermore demonstrate that the degree of disassortative mixing also has a great effect in the presence of explosive synchronization.