Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for asset graphs based on distance thresholds and diverse periods of time, so that it is then possible to analyze how clusters are formed according to correlations among indices and how they evolve in time, particularly during times of financial crises. Further analysis is made on the eigenvectors corresponding to the second highest eigenvalues of the correlation matrices, revealing a structure peculiar to markets that operate in different time zones. We also study the survivability of connections and of clusters through time and the influence of noise in centrality measures applied to the networks of financial indices. The results show how the world's main stock market indices evolved in the last few decades with respect to their clustering structure, how their connections survive in time, and which indices are more central, according to different criteria. In particular, we witness the early formation and evolution of two main clusters, an American and an European one, the formation of a Pacific Asian cluster, and later on, of an Arab cluster. This analysis complements previous studies of the interdependencies of stock markets worldwide.