Based on a general dynamical model for disaster spreading, in different network structures, i.e. in Erdos-Renyi network, scale-free network and small world network, the influences of network centrality on the speed and trend of disaster spreading are analyzed by simulation. By changing the initial spreading condition, the influence of initial state on the spreading efficiency is analyzed. In this paper the differences between final disaster spreading state are mainly discussed based on four initial vertex-choosing strategies. For the four strategies, it is shown that there are apparent differences. Complex network has a strong ability to resist random attacks but is is fragile to resist intentional attacks. However, the three networks show different degrees of fragility. And then, the theoretical analysis results are verified in an actual network.