  Centrality rankings such as degree, closeness, betweenness, Katz, PageRank,
etc. are commonly used to identify critical nodes in a graph. These methods are
based on two assumptions that restrict their wider applicability. First, they
assume the exact topology of the network is available. Secondly, they do not
take into account the activity over the network and only rely on its topology.
However, in many applications, the network is autonomous, vast, and
distributed, and it is hard to collect the exact topology. At the same time,
the underlying pairwise activity between node pairs is not uniform and node
criticality strongly depends on the activity on the underlying network.
  In this paper, we propose active betweenness cardinality, as a new measure,
where the node criticalities are based on not the static structure, but the
activity of the network. We show how this metric can be computed efficiently by
using only local information for a given node and how we can find the most
critical nodes starting from only a few nodes. We also show how this metric can
be used to monitor a network and identify failed nodes.We present experimental
results to show effectiveness by demonstrating how the failed nodes can be
identified by measuring active betweenness cardinality of a few nodes in the
system.
