  We show that the global balance index of financial correlation networks can
be used as a systemic risk measure. We define the global balance of a network
starting from a diffusive process that describes how the information spreads
across nodes in a network, providing an alternative derivation to the usual
combinatorial one. The steady state of this process is the solution of a linear
system governed by the exponential of the replication matrix of the process. We
provide a bridge between the numerical stability of this linear system,
measured by the condition number in an opportune norm, and the structural
predictability of the underlying signed network. The link between the condition
number and related systemic risk measures, such as the market rank indicators,
allows the global balance index to be interpreted as a new systemic risk
measure. A comprehensive empirical application to real financial data finally
confirms that the global balance index of the financial correlation network
represents a valuable and effective systemic risk indicator.
