Before revision:  The eigenvalue decomposition of a correlation matrix into partial correlations - market, group and random modes, enables identification of dominant stocks or "influential leaders" and sectors or "communities". The correlation-based network of leaders and communities changes with time, especially during market events like crashes , bubbles, etc.
After revision:  The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market events like crashes , bubbles, etc.