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 kth 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.
