Degree stability of a minimum spanning tree of price return and volatility

We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time window of fixed length $T$. We find that the minimum spanning tree of asset return is characterized by stock degree values, which are more stable in time than the ones obtained by analyzing a minimum spanning tree computed starting from volatility time series. Our analysis also shows that the degree of stocks has a very slow dynamics with a time-scale of several years in both cases.