  Maximum spanning tree (MST) is a popular tool in market network analysis.
Large number of publications are devoted to the MST calculation and it's
interpretation for particular stock markets. However, much less attention is
payed in the literature to the analysis of uncertainty of obtained results. In
the present paper we suggest a general framework to measure uncertainty of MST
identification. We study uncertainty in the framework of the concept of random
variable network (RVN). We consider different correlation based networks in the
large class of elliptical distributions. We show that true MST is the same in
three networks: Pearson correlation network, Fechner correlation network, and
Kendall correlation network. We argue that among different measures of
uncertainty the FDR (False Discovery Rate) is the most appropriated for MST
identification. We investigate FDR of Kruskal algorithm for MST identification
and show that reliability of MST identification is different in these three
networks. In particular, for Pearson correlation network the FDR essentially
depends on distribution of stock returns. We prove that for market network with
Fechner correlation the FDR is non sensitive to the assumption on stock's
return distribution. Some interesting phenomena are discovered for Kendall
correlation network. Our experiments show that FDR of Kruskal algorithm for MST
identification in Kendall correlation network weakly depend on distribution and
at the same time the value of FDR is almost the best in comparison with MST
identification in other networks. These facts are important in practical
applications.
