Emergence of frustration signals systemic risk.

We show that the emergence of systemic risk in complex systems can be understood from the evolution of functional networks representing interactions inferred from fluctuation correlations between macroscopic observables. Specifically, we analyze the long-term collective dynamics in the New York Stock Exchange, the largest financial market in the world, for almost a century and show that periods marked by systemic crisis are associated with emergence of frustration. This is indicated by the loss of structural balance in the networks of interaction between stocks. Moreover, the mesoscopic organization of the networks during these periods exhibits prominent core-periphery organization. This suggests an increased degree of coherence in the collective dynamics of the system, which is reinforced by our observation of the transition to delocalization in the dominant eigenmodes when the systemic risk builds up. While frustration has been associated with phase transitions in physical systems such as spin glasses, its role as a signal for systemic risk buildup leading to severe crisis as shown here provides a novel perspective into the dynamical processes leading to catastrophic failures in complex systems.