  We explore the dependence structure in the sampled sequence of large
networks. We consider randomized algorithms to sample the nodes and study
extremal properties in any associated stationary sequence of characteristics of
interest like node degrees, number of followers or income of the nodes in
Online Social Networks etc, which satisfy two mixing conditions. Several useful
extremes of the sampled sequence like $k$th largest value, clusters of
exceedances over a threshold, first hitting time of a large value etc are
investigated. We abstract the dependence and the statistics of extremes into a
single parameter that appears in Extreme Value Theory, called extremal index
(EI). In this work, we derive this parameter analytically and also estimate it
empirically. We propose the use of EI as a parameter to compare different
sampling procedures. As a specific example, degree correlations between
neighboring nodes are studied in detail with three prominent random walks as
sampling techniques.
