  Despite the prevalence of community detection algorithms, relatively less
work has been done on understanding whether a network is indeed modular and how
resilient the community structure is under perturbations. To address this
issue, we propose a new vertex-based metric called "permanence", that can
quantitatively give an estimate of the community-like structure of the network.
  The central idea of permanence is based on the observation that the strength
of membership of a vertex to a community depends upon the following two
factors: (i) the distribution of external connectivity of the vertex to
individual communities and not the total external connectivity, and (ii) the
strength of its internal connectivity and not just the total internal edges.
  In this paper, we demonstrate that compared to other metrics, permanence
provides (i) a more accurate estimate of a derived community structure to the
ground-truth community and (ii) is more sensitive to perturbations in the
network. As a by-product of this study, we have also developed a community
detection algorithm based on maximizing permanence. For a modular network
structure, the results of our algorithm match well with ground-truth
communities.
