Understanding stock market instability is a key question in financial managementas practitioners seek to forecast breakdowns in asset co-movements which exposeportfolios to rapid and devastating collapses in value. The structure of theseco-movements can be described as a graph where companies are represented bynodes and edges capture correlations between their price movements. Learning atimely indicator of co-movement breakdowns (manifested as modifications in thegraph structure) is central in understanding both financial stability and volatilityforecasting. We propose to use the edge-reconstruction accuracy of a graph auto-encoder (GAE) as an indicator for how spatially homogeneous connections betweenassets are, which, based on financial network literature, we use as a proxy to infermarket volatility. Our experiments on the S&P 500 over the 2015-2022 period showthat higher GAE reconstruction error values are correlated with higher volatility.We also show that out-of-sample autoregressive modeling of volatility is improvedby the addition of the proposed measure. Our paper contributes to the literatureof machine learning in finance particularly in the context of understanding stockmarket instability.