  In this paper, we study the crucial elements of complex networks, namely
nodes, and edges and their properties such as their community structure, which
play an important role in dictating the robustness of the network towards
structural perturbations. Specifically, we want to identify all vital nodes,
which when removed would lead to a large change in the underlying community
structure of the network. This problem is extremely important because the
community structure of a network allows deep underlying insights into how
function of a network and its topology affect each other. Moreover, it even
provides a way to condense large graphs into smaller graphs where each
community acts as a meta node and hence aids in easier network analysis. If
this community structure was to be compromised by either accidental or
intentional perturbations to the network, that would make such analysis
difficult. Since the problem of identifying such vital nodes is computationally
intractable, we propose some heuristics that allow us to find solutions close
to the optimal solution. To certify the effectiveness of our approach, we first
test these heuristics on small networks, and then move to larger networks to
show that we achieve similar results. The results reveal that the proposed
approaches are effective to analyze the vulnerability of communities in graphs
irrespective of their size and scale. From the application point of view, we
show that the proposed algorithm is scalable and can be applied to the
information diffusion task to curtail the spread of active nodes which was
observed empirically. Additionally, we show the performance of our algorithm
through an extrinsic evaluation -- we employ two tasks, like prediction and
information diffusion, and show that the effect of our algorithm on these tasks
is higher than the other baselines.
